Higher partial waves in ! "# interaction . Albert Feijoo Aliau - - PowerPoint PPT Presentation
Higher partial waves in ! "# interaction . Albert Feijoo Aliau Nuclear Physics Institute, Rez, Czech Republic Collaborators: ngels Ramos and Volodymyr Magas Universitat de Barcelona, ICCUB Daniel Gazda Nuclear Physics Institute, Rez,
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THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
Collaborators: Albert Feijoo Aliau Nuclear Physics Institute, Rez, Czech Republic Àngels Ramos and Volodymyr Magas Universitat de Barcelona, ICCUB Daniel Gazda Nuclear Physics Institute, Rez, Czech Republic
Introduction: Theoretical Framework and Historical Background
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THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
!" !# $% &" $' &# 1255 MeV 1810 MeV Aim: Study of the meson-baryon interaction in the S=-1 sector at low energies. 10 channels involved in this sector: $(), + $,-, !,", !,#,, !.#(, !(#., &", &#,, $.'(, $,', Interaction: QCD is a gauge theory which describes the strong interaction governed by the effects of the color charge of its carriers: quarks and gluons. Perturbative QCD is inappropriate to treat low energy hadron interactions. Chiral Perturbation Theory (ChPT) is an effective theory with hadrons as degrees of freedom which respects the symmetries of QCD.
But it is not so straight forward …
Introduction: Theoretical Framework and Historical Background
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THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
! "# interaction is dominated by the presence of the $ %&'( resonance, located only 27 MeV below the Kbar-N threshold. à A nonperturbative resummation is needed!!!
(UChPT) in coupled channels. The pioneering work -- Kaiser, Siegel, Weise, NP A594 (1995) 325
(2003).
V.K. Magas, E. Oset, A. Ramos, Phys. Rev. Lett. 95, 052301 (2005).
All of them obtaining in general similar features:
)* scattering data reproduced very satisfactorily
Introduction: Theoretical Framework and Historical Background
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THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
The energy shift and width of the 1s state in kaonic hydrogen measured by SIDDHARTA@DAΦNE fixes the !"# scattering length with a 20% precision!!!
Photoproduction $# ⟶ !&'( data by the CLAS@Jlab provided detailed line shape results of the Λ(1405)
Zhi-Hui Guo, J. A. Oller, Phys. Rev. C 87, 035202 (2013).
A. Feijoo, V. Magas, A. Ramos, Phys. Rev. C 92, 015206 (2015).
This topic has experienced a renewed interest after recent experimental advances:
Motivation: Evolution of the model
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THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
We focus on processes which filter isospin could provide more constraints in order to get more reliable values of NLO coefficients.
Observable Points Observable Points σK−p→K−p 23 σK−p→ ¯
K0n
9 σK−p→π0Λ 3 σK−p→π0Σ0 3 σK−p→π−Σ+ 20 σK−p→π+Σ− 28 σK−p→ηΣ0 9 σK−p→ηΛ 49 σK−p→K+Ξ− 46 σK−p→K0Ξ0 29 γ 1 ∆E1s 1 Rn 1 Γ1s 1 Rc 1
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THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
Vij = V
W T
ij
+ V
D
ij + V
C
ij + V
NLO
ij
= ⇒ T = (1 − V G)−1V = ⇒ Tij
<latexit sha1_base64="bSkfiuiUhTxMs2QWMKJA5u2ON/8=">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</latexit><latexit sha1_base64="xzWmobhVTRd9IUnI+1YIAkBblS4=">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</latexit><latexit sha1_base64="xzWmobhVTRd9IUnI+1YIAkBblS4=">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</latexit><latexit sha1_base64="TPj/nruKGTf8/fSjEUmyv/OFq98=">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</latexit>2 new fits were performed:
Only S-wave contribution is taken into account
Motivation: Evolution of the model
7
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
Vij = V
W T
ij
+ V
D
ij + V
C
ij + V
NLO
ij
= ⇒ T = (1 − V G)−1V = ⇒ Tij
<latexit sha1_base64="bSkfiuiUhTxMs2QWMKJA5u2ON/8=">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</latexit><latexit sha1_base64="xzWmobhVTRd9IUnI+1YIAkBblS4=">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</latexit><latexit sha1_base64="xzWmobhVTRd9IUnI+1YIAkBblS4=">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</latexit><latexit sha1_base64="TPj/nruKGTf8/fSjEUmyv/OFq98=">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</latexit>2 new fits were performed:
a) Inclusion of high spin and high mass resonances allows us to study the stability of the NLO parameters. b) It also simulates the contributions of higher angular momenta of the other channels via rescattering in the energy regime above !" threshold.
K $′& , η $′& !( $& p )& Ξ )+& , Λ )+&
12.3, 14.5 16.7
3
Y= 4 89:; , < =;>; , < ==?;
Sharov, Korotkikh, Lanskoy, EPJA 47 (2011) 109 Jackson, Oh, Haberzettl and Nakayama,Phys. Rev. C 91, 065208 (2015) Feijoo, Magas, Ramos, Phys. Rev. C 92, 015206 (2015)
T tot
ij
= T BS
ij
+ 1 p4MpMΞ X
JP
T JP
ij , JP = 3/2+, 5/2−, 7/2+
<latexit sha1_base64="HamHwBJsS4UZgPqkDmzUC6oENPA=">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</latexit><latexit sha1_base64="HamHwBJsS4UZgPqkDmzUC6oENPA=">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</latexit><latexit sha1_base64="HamHwBJsS4UZgPqkDmzUC6oENPA=">ACUXicbVFdSyMxFM2Mr1q6PvgSLINitM37gvgiL4sgVLbVQqcdMjHTRjMfm9xZKCH/0Dd92Z+yPpkZK7jqJYRz7jkXck+iXHAFnvfXcWdmv8zNL3ytLS4tr6zW175dqayQlHVpJjLZi4higqesCxwE6+WSkSQS7Dq6Oyv16z9MKp6lHZjkbJCQUcpjTgnYVlhPO6Hmt2aoIQNzjDtDfrLVK2guRPEklDtGx2o3xL0wUWYX4RBjxsTqCIJ9fmwbV7nK2JwEwfVsex4f3dvuNM8tPf35lGJa7Ww3vBaXlX4I/CnoIGm1Q7r98FNRouEpUAFUarvezkMNJHAqWCmFhSK5YTekRHrW5iShKmBrnIxeCvOJIYxwxV/69UkUWqSRNaTEBir91rZ/EzrFxD/Gie5gWwlFqL1eJCYMhwGS+4ZJREBMLCJXcvhLTMbExgv2Ecn3/bIfwdVey/da/uVB4+R0GsQC2kCbaBv56AidoJ+ojbqIokf05Mw4s86D89FrvtidZ3pzDr6r9zFZ693rwU=</latexit><latexit sha1_base64="HamHwBJsS4UZgPqkDmzUC6oENPA=">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</latexit>T tot
ij
= T BS
ij
+ 1 p 4MpMΛ T 3/2+
ij
<latexit sha1_base64="rVNDH4algYW8Pr72qg0j9HQpMeM=">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</latexit><latexit sha1_base64="rVNDH4algYW8Pr72qg0j9HQpMeM=">ACMnicbVDNThsxGPQCpWFLIdAjF4sICYkq3aWR4IUpZceiACRAFI2WXkdLzHx/mB/ixRZfqv2LfoCwAkBNx4CJ6RSgX6n8cx8nzwT5YIr8LxrZ2Z27sP8x9KC+2nx89JyeWX1RGWFpKxNM5HJs4goJnjK2sBsLNcMpJEgp1Gwx9j/fSKScWztAWjnHUTcp7ymFMClgrLB61Q8wvT05CB2cOtnm4cmwkVfN0KYkmo9o0O1KUEXWuGeTM9u31PjHW8HdXf/+2bXpbxnXdsFzxqt5k8HvgT0EFTecwLP8J+hktEpYCFUSpju/l0NVEAqeCGTcoFMsJHZJz1rEwJQlTXT0JbvBGnEkMA4Yn73+9miRKjZLIehICA/VWG5P/0zoFxLtdzdO8AJZSa7FaXAgMGR73h/tcMgpiZAGhktfYjogtiewLY/j+2/Dvgcn21Xfq/pHtUq9MS2ihNbQOtpEPtpBdfQTHaI2oug3ukUP6NH5dw4d879i3XGme58Qa/GeXoG6tGqWQ=</latexit><latexit sha1_base64="rVNDH4algYW8Pr72qg0j9HQpMeM=">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</latexit><latexit sha1_base64="rVNDH4algYW8Pr72qg0j9HQpMeM=">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</latexit>Only for 3(@ ⟶ 3B reactions: Only for 3(@ ⟶ 54 reaction:
Motivation: Evolution of the model
8
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
Prediction/reproduction for Isospin filtering processes: !"
#$ ⟶ !&'# reaction (pure ( = 1 process)
J-Lab proposal for the secondary !" beam
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
|TK
Mai-Meissner 4 Mai-Meissner 2 Guo-Oller 2 Guo-Oller 1 Cieply-Smejkal Ikeda-Hyodo-Weise Ramos-Magas-Feijoo AMADEUS (exp)
1800 2000 2200 2400 2600 w [MeV] 0.05 0.1 0.15 0.2 0.25 σ (K
Lp ---> K +Ξ 0) [mb]
WT+NLO [31] WT+Born+NLO [32] WT+Born+NLO WT+Born+NLO+RES
AMADEUS collaboration, KLOE detector at DAFNE
!+, ⟶ -+Λ reaction (pure ( = 1 process)
Motivation: Evolution of the model
9
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
Pole content (WT+Born+NLO)
0− ⊕ 1
2 + interaction in (I, S) = (0, −1) sector
Pole |gπΣ| |g ¯
KN| |gηΛ| |gKΞ|
Λ(1405) 1419+16
−22 − i 71+24 −31
3.40 2.98 1.10 0.65 1420+15
−21 − i 27+18 −11
2.31 3.51 1.26 0.36 Λ(1670) 1675+10
−11 − i 31+4 −7
0.47 0.59 1.74 3.71 0− ⊕ 1
2 + interaction in (I, S) = (1, −1) sector
Pole |gπΛ| |gπΣ| |g ¯
KN| |gηΣ| |gKΞ|
Σ∗ 1701+16
−1 − i 170+2 −7 1.96
0.47 1.21 0.36 0.98
Motivation: Evolution of the model
10
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
1300 1350 1400 1450 1500 Re zp (MeV) 50 100 150 200
Roca - Oset Guo - Oller (fit I) Guo - Oller (fit II) Ikeda - Hyodo -Wiese (NLO) Mai - Meissner (fit II) Mai - Meissner (fit IV) Cieply - Smejkal (NLO) Shevchenco (two-pole) Our Model
Pole content (WT+Born+NLO)
0− ⊕ 1
2 + interaction in (I, S) = (0, −1) sector
Pole |gπΣ| |g ¯
KN| |gηΛ| |gKΞ|
Λ(1405) 1419+16
−22 − i 71+24 −31
3.40 2.98 1.10 0.65 1420+15
−21 − i 27+18 −11
2.31 3.51 1.26 0.36 Λ(1670) 1675+10
−11 − i 31+4 −7
0.47 0.59 1.74 3.71 0− ⊕ 1
2 + interaction in (I, S) = (1, −1) sector
Pole |gπΛ| |gπΣ| |g ¯
KN| |gηΣ| |gKΞ|
Σ∗ 1701+16
−1 − i 170+2 −7 1.96
0.47 1.21 0.36 0.98
Motivation: Evolution of the model
11
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
γ Rn Rc ap(K−p → K−p) ∆E1s Γ1s Ikeda-Hyodo-Weise (NLO) [23] 2.37 0.19 0.66 −0.70 + i 0.89 306 591 Guo-Oller (fit I + II) [25] 2.36+0.24
−0.23
0.188+0.028
−0.029
0.661+0.012
−0.011
(−0.69 ± 0.16) + i (0.94 ± 0.11) 308 ± 56 619 ± 73 Mizutani et al (Model s) [26] 2.40 0.189 0.645 −0.69 + i 0.89 304 591 Mai-Meissner (fit 4) [29] 2.38+0.09
−0.10
0.191+0.013
−0.017
0.667+0.006
−0.005
288+34
−32
572+39
−38
Cieply-Smejkal (NLO) [76] 2.37 0.191 0.660 −0.73 + i 0.85 310 607 Shevchenko (two-pole Model) [77] 2.36 −0.74 + i 0.90 308 602 WT+Born+NLO 2.36+0.03
−0.03
0.188+0.010
−0.011
0.659+0.005
−0.002
−0.65+0.02
−0.08 + i 0.88+0.02 −0.05
288+23
−8
588+9
−40
WT+NLO+Born+RES 2.36 0.189 0.661 −0.64 + i 0.87 283 587 Exp. 2.36 ± 0.04 0.189 ± 0.015 0.664 ± 0.011 (−0.66 ± 0.07) + i (0.81 ± 0.15) 283 ± 36 541 ± 92
Threshold observables obtained from our fits and from other recent studies
Motivation: Evolution of the model
12
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer. 1700 1800 1900 2000 2100 2200 0.5 1 1.5 2 σ(K
1700 1800 1900 2000 2100 2200 0.5 1 1.5 2 σ(K
0) [mb]
1800 2000 2200 2400 2600
w [MeV]
0.05 0.1 0.15 σ(K
0Ξ 0) [mb] WT+Born+NLO WT+Born+NLO+RES
1800 2000 2200 2400 2600
w [MeV]
0.05 0.1 0.15 0.2 0.25 σ(K
+Ξ
WT+Born+NLO WT+Born+NLO+RES
1660 1680 1700 0.5 1 1.5 2
Total cross sections WT+Born+NLO+RES improves the description of the experimental data Inclusion of higher partial waves could play similar role What about dynamically generating resonances with such contributions?
Formalism: Effective Chiral Lagrangian
13
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
MB = h ¯
MB(B, U) + L(2) MB(B, U)
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Formalism: Effective Chiral Lagrangian
14
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
MB(B, U) + L(2) MB(B, U)
<latexit sha1_base64="x656Dim2un4bE8RG7XfE6WXtEpA=">ACOXicbZDLSgMxFIYz9VbrbdSlm2ARWpQyUwTdCKVuXChUsBdoa8mkZ9rQzIUkI5ShT6aP4Au41JWoO1/AtJ1Fbfuv/vzfHzjnOCFnUlnWm5FaWV1b30hvZra2d3b3zP2DmgwiQaFKAx6IhkMkcOZDVTHFoREKIJ7Doe4Mrse8/gRCsB/UMQ2h7p+cxlCgdcwa1mp5RPUp4fHt6DEG1x3lymfV/NVMnOnEd7isac7OT+npUlpMaMfMWgVrIrxo7MRkUaJKx3xtdQMaeAryomUTdsKVTsmQjHKYZRpRJCQgekB01tfeKBbMeT/Uf4xA0EVn3Ak/dsNyaelEP0Z3xuHKejcNlrBkp97IdMz+MFPhUVzRzI45VgMdnxF0mgCo+1IZQwfSUmPaJIFTpY2f0+vb8soumVizYVsG+P8+Wyskh0ugIHaMcstEFKqEbVEFVRNEL+kDf6Md4Nt6NT+NrWk0ZyZ9D9E/G7x9rIqmG</latexit><latexit sha1_base64="x656Dim2un4bE8RG7XfE6WXtEpA=">ACOXicbZDLSgMxFIYz9VbrbdSlm2ARWpQyUwTdCKVuXChUsBdoa8mkZ9rQzIUkI5ShT6aP4Au41JWoO1/AtJ1Fbfuv/vzfHzjnOCFnUlnWm5FaWV1b30hvZra2d3b3zP2DmgwiQaFKAx6IhkMkcOZDVTHFoREKIJ7Doe4Mrse8/gRCsB/UMQ2h7p+cxlCgdcwa1mp5RPUp4fHt6DEG1x3lymfV/NVMnOnEd7isac7OT+npUlpMaMfMWgVrIrxo7MRkUaJKx3xtdQMaeAryomUTdsKVTsmQjHKYZRpRJCQgekB01tfeKBbMeT/Uf4xA0EVn3Ak/dsNyaelEP0Z3xuHKejcNlrBkp97IdMz+MFPhUVzRzI45VgMdnxF0mgCo+1IZQwfSUmPaJIFTpY2f0+vb8soumVizYVsG+P8+Wyskh0ugIHaMcstEFKqEbVEFVRNEL+kDf6Md4Nt6NT+NrWk0ZyZ9D9E/G7x9rIqmG</latexit><latexit sha1_base64="x656Dim2un4bE8RG7XfE6WXtEpA=">ACOXicbZDLSgMxFIYz9VbrbdSlm2ARWpQyUwTdCKVuXChUsBdoa8mkZ9rQzIUkI5ShT6aP4Au41JWoO1/AtJ1Fbfuv/vzfHzjnOCFnUlnWm5FaWV1b30hvZra2d3b3zP2DmgwiQaFKAx6IhkMkcOZDVTHFoREKIJ7Doe4Mrse8/gRCsB/UMQ2h7p+cxlCgdcwa1mp5RPUp4fHt6DEG1x3lymfV/NVMnOnEd7isac7OT+npUlpMaMfMWgVrIrxo7MRkUaJKx3xtdQMaeAryomUTdsKVTsmQjHKYZRpRJCQgekB01tfeKBbMeT/Uf4xA0EVn3Ak/dsNyaelEP0Z3xuHKejcNlrBkp97IdMz+MFPhUVzRzI45VgMdnxF0mgCo+1IZQwfSUmPaJIFTpY2f0+vb8soumVizYVsG+P8+Wyskh0ugIHaMcstEFKqEbVEFVRNEL+kDf6Md4Nt6NT+NrWk0ZyZ9D9E/G7x9rIqmG</latexit><latexit sha1_base64="x656Dim2un4bE8RG7XfE6WXtEpA=">ACOXicbZDLSgMxFIYz9VbrbdSlm2ARWpQyUwTdCKVuXChUsBdoa8mkZ9rQzIUkI5ShT6aP4Au41JWoO1/AtJ1Fbfuv/vzfHzjnOCFnUlnWm5FaWV1b30hvZra2d3b3zP2DmgwiQaFKAx6IhkMkcOZDVTHFoREKIJ7Doe4Mrse8/gRCsB/UMQ2h7p+cxlCgdcwa1mp5RPUp4fHt6DEG1x3lymfV/NVMnOnEd7isac7OT+npUlpMaMfMWgVrIrxo7MRkUaJKx3xtdQMaeAryomUTdsKVTsmQjHKYZRpRJCQgekB01tfeKBbMeT/Uf4xA0EVn3Ak/dsNyaelEP0Z3xuHKejcNlrBkp97IdMz+MFPhUVzRzI45VgMdnxF0mgCo+1IZQwfSUmPaJIFTpY2f0+vb8soumVizYVsG+P8+Wyskh0ugIHaMcstEFKqEbVEFVRNEL+kDf6Md4Nt6NT+NrWk0ZyZ9D9E/G7x9rIqmG</latexit>Lagrangian: à derive an interaction kernel Vij
MB = h ¯
Weinberg-Tomozawa term (WT)
the pseudoscalar meson
V W T
ij
= − NiNj
4f 2 Cij
n (2√s − Mi − Mj)†s0
f s 0 + 2√s+Mi+Mj (Ei+Mi)(Ej+Mj) †s0 f
[~ qj · ~ qi + i(~ qj × ~ qi) · ~ ] s
Formalism: Effective Chiral Lagrangian
15
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
MB = h ¯
MB(B, U) + L(2) MB(B, U)
<latexit sha1_base64="x656Dim2un4bE8RG7XfE6WXtEpA=">ACOXicbZDLSgMxFIYz9VbrbdSlm2ARWpQyUwTdCKVuXChUsBdoa8mkZ9rQzIUkI5ShT6aP4Au41JWoO1/AtJ1Fbfuv/vzfHzjnOCFnUlnWm5FaWV1b30hvZra2d3b3zP2DmgwiQaFKAx6IhkMkcOZDVTHFoREKIJ7Doe4Mrse8/gRCsB/UMQ2h7p+cxlCgdcwa1mp5RPUp4fHt6DEG1x3lymfV/NVMnOnEd7isac7OT+npUlpMaMfMWgVrIrxo7MRkUaJKx3xtdQMaeAryomUTdsKVTsmQjHKYZRpRJCQgekB01tfeKBbMeT/Uf4xA0EVn3Ak/dsNyaelEP0Z3xuHKejcNlrBkp97IdMz+MFPhUVzRzI45VgMdnxF0mgCo+1IZQwfSUmPaJIFTpY2f0+vb8soumVizYVsG+P8+Wyskh0ugIHaMcstEFKqEbVEFVRNEL+kDf6Md4Nt6NT+NrWk0ZyZ9D9E/G7x9rIqmG</latexit><latexit sha1_base64="x656Dim2un4bE8RG7XfE6WXtEpA=">ACOXicbZDLSgMxFIYz9VbrbdSlm2ARWpQyUwTdCKVuXChUsBdoa8mkZ9rQzIUkI5ShT6aP4Au41JWoO1/AtJ1Fbfuv/vzfHzjnOCFnUlnWm5FaWV1b30hvZra2d3b3zP2DmgwiQaFKAx6IhkMkcOZDVTHFoREKIJ7Doe4Mrse8/gRCsB/UMQ2h7p+cxlCgdcwa1mp5RPUp4fHt6DEG1x3lymfV/NVMnOnEd7isac7OT+npUlpMaMfMWgVrIrxo7MRkUaJKx3xtdQMaeAryomUTdsKVTsmQjHKYZRpRJCQgekB01tfeKBbMeT/Uf4xA0EVn3Ak/dsNyaelEP0Z3xuHKejcNlrBkp97IdMz+MFPhUVzRzI45VgMdnxF0mgCo+1IZQwfSUmPaJIFTpY2f0+vb8soumVizYVsG+P8+Wyskh0ugIHaMcstEFKqEbVEFVRNEL+kDf6Md4Nt6NT+NrWk0ZyZ9D9E/G7x9rIqmG</latexit><latexit sha1_base64="x656Dim2un4bE8RG7XfE6WXtEpA=">ACOXicbZDLSgMxFIYz9VbrbdSlm2ARWpQyUwTdCKVuXChUsBdoa8mkZ9rQzIUkI5ShT6aP4Au41JWoO1/AtJ1Fbfuv/vzfHzjnOCFnUlnWm5FaWV1b30hvZra2d3b3zP2DmgwiQaFKAx6IhkMkcOZDVTHFoREKIJ7Doe4Mrse8/gRCsB/UMQ2h7p+cxlCgdcwa1mp5RPUp4fHt6DEG1x3lymfV/NVMnOnEd7isac7OT+npUlpMaMfMWgVrIrxo7MRkUaJKx3xtdQMaeAryomUTdsKVTsmQjHKYZRpRJCQgekB01tfeKBbMeT/Uf4xA0EVn3Ak/dsNyaelEP0Z3xuHKejcNlrBkp97IdMz+MFPhUVzRzI45VgMdnxF0mgCo+1IZQwfSUmPaJIFTpY2f0+vb8soumVizYVsG+P8+Wyskh0ugIHaMcstEFKqEbVEFVRNEL+kDf6Md4Nt6NT+NrWk0ZyZ9D9E/G7x9rIqmG</latexit><latexit sha1_base64="x656Dim2un4bE8RG7XfE6WXtEpA=">ACOXicbZDLSgMxFIYz9VbrbdSlm2ARWpQyUwTdCKVuXChUsBdoa8mkZ9rQzIUkI5ShT6aP4Au41JWoO1/AtJ1Fbfuv/vzfHzjnOCFnUlnWm5FaWV1b30hvZra2d3b3zP2DmgwiQaFKAx6IhkMkcOZDVTHFoREKIJ7Doe4Mrse8/gRCsB/UMQ2h7p+cxlCgdcwa1mp5RPUp4fHt6DEG1x3lymfV/NVMnOnEd7isac7OT+npUlpMaMfMWgVrIrxo7MRkUaJKx3xtdQMaeAryomUTdsKVTsmQjHKYZRpRJCQgekB01tfeKBbMeT/Uf4xA0EVn3Ak/dsNyaelEP0Z3xuHKejcNlrBkp97IdMz+MFPhUVzRzI45VgMdnxF0mgCo+1IZQwfSUmPaJIFTpY2f0+vb8soumVizYVsG+P8+Wyskh0ugIHaMcstEFKqEbVEFVRNEL+kDf6Md4Nt6NT+NrWk0ZyZ9D9E/G7x9rIqmG</latexit>Lagrangian: à derive an interaction kernel Vij
1 2
C
ij = V
C
ij (D, F)
<latexit sha1_base64="z8tid280bIFl7LH6euRnPHaRCYE=">ACI3icfVBNS0JBFJ1nX2ZfVs2QxIYhLwXQW0CyYiWBvkBajJvOrkvA9m7gvk4c+pP5OrqKBF/6XR3qI0OovLufecgTnHDaXQaNsfVmphcWl5Jb2aWVvf2NzKbu9UdRApDhUeyEDVXaZBCh8qKFBCPVTAPFdCzR2UJnrtAZQWgX+LwxBaHuv5ois4Q3NqZ4vVu7ipuRIhJhOHEmhp1I7F/ej8XzV/eXR12M7m7I9BZ0nTkJyJEG5nR03OwGPCRS6Z1w7FDbMVMoeASRplmpCFkfMB60DUZx7oVjxNOqIH3UBR7AOd7j+9MfO0Hnqu8XgM+3pWmxz/0hoRds9asfDCMHnxmK0biQpBnRSGO0IBRzl0BmOjC/pLzPFONoas2Y+M5s2HlSPS4dsG5OckVL5Ii0mSP7JM8cgpKZJrUiYVwskTGZM38m49Ws/Wi/X6bU1ZyZtd8gvW5xeD2aXk</latexit><latexit sha1_base64="z8tid280bIFl7LH6euRnPHaRCYE=">ACI3icfVBNS0JBFJ1nX2ZfVs2QxIYhLwXQW0CyYiWBvkBajJvOrkvA9m7gvk4c+pP5OrqKBF/6XR3qI0OovLufecgTnHDaXQaNsfVmphcWl5Jb2aWVvf2NzKbu9UdRApDhUeyEDVXaZBCh8qKFBCPVTAPFdCzR2UJnrtAZQWgX+LwxBaHuv5ois4Q3NqZ4vVu7ipuRIhJhOHEmhp1I7F/ej8XzV/eXR12M7m7I9BZ0nTkJyJEG5nR03OwGPCRS6Z1w7FDbMVMoeASRplmpCFkfMB60DUZx7oVjxNOqIH3UBR7AOd7j+9MfO0Hnqu8XgM+3pWmxz/0hoRds9asfDCMHnxmK0biQpBnRSGO0IBRzl0BmOjC/pLzPFONoas2Y+M5s2HlSPS4dsG5OckVL5Ii0mSP7JM8cgpKZJrUiYVwskTGZM38m49Ws/Wi/X6bU1ZyZtd8gvW5xeD2aXk</latexit><latexit sha1_base64="z8tid280bIFl7LH6euRnPHaRCYE=">ACI3icfVBNS0JBFJ1nX2ZfVs2QxIYhLwXQW0CyYiWBvkBajJvOrkvA9m7gvk4c+pP5OrqKBF/6XR3qI0OovLufecgTnHDaXQaNsfVmphcWl5Jb2aWVvf2NzKbu9UdRApDhUeyEDVXaZBCh8qKFBCPVTAPFdCzR2UJnrtAZQWgX+LwxBaHuv5ois4Q3NqZ4vVu7ipuRIhJhOHEmhp1I7F/ej8XzV/eXR12M7m7I9BZ0nTkJyJEG5nR03OwGPCRS6Z1w7FDbMVMoeASRplmpCFkfMB60DUZx7oVjxNOqIH3UBR7AOd7j+9MfO0Hnqu8XgM+3pWmxz/0hoRds9asfDCMHnxmK0biQpBnRSGO0IBRzl0BmOjC/pLzPFONoas2Y+M5s2HlSPS4dsG5OckVL5Ii0mSP7JM8cgpKZJrUiYVwskTGZM38m49Ws/Wi/X6bU1ZyZtd8gvW5xeD2aXk</latexit><latexit sha1_base64="z8tid280bIFl7LH6euRnPHaRCYE=">ACI3icfVBNS0JBFJ1nX2ZfVs2QxIYhLwXQW0CyYiWBvkBajJvOrkvA9m7gvk4c+pP5OrqKBF/6XR3qI0OovLufecgTnHDaXQaNsfVmphcWl5Jb2aWVvf2NzKbu9UdRApDhUeyEDVXaZBCh8qKFBCPVTAPFdCzR2UJnrtAZQWgX+LwxBaHuv5ois4Q3NqZ4vVu7ipuRIhJhOHEmhp1I7F/ej8XzV/eXR12M7m7I9BZ0nTkJyJEG5nR03OwGPCRS6Z1w7FDbMVMoeASRplmpCFkfMB60DUZx7oVjxNOqIH3UBR7AOd7j+9MfO0Hnqu8XgM+3pWmxz/0hoRds9asfDCMHnxmK0biQpBnRSGO0IBRzl0BmOjC/pLzPFONoas2Y+M5s2HlSPS4dsG5OckVL5Ii0mSP7JM8cgpKZJrUiYVwskTGZM38m49Ws/Wi/X6bU1ZyZtd8gvW5xeD2aXk</latexit>D
ij = V
D
ij (D, F)
<latexit sha1_base64="Igjn3htqGMa+w6xjh/e+ny+h0h0=">ACI3icfVBNS0JBFJ1nX2ZfVs2QxIYhLwXQW0CKYmWBvkBajJvOrkvA9m7gvk4c+pP5OrqKBF/6XR3qI0OovLufecgTnHDaXQaNsfVmphcWl5Jb2aWVvf2NzKbu9UdRApDhUeyEDVXaZBCh8qKFBCPVTAPFdCzR1cTvTaAygtAv8WhyG0PNbzRVdwhubUzhard3FTcyVCTCYOJdDSqB2L+9H5v2q+dHR12M7m7I9BZ0nTkJyJEG5nR03OwGPCRS6Z1w7FDbMVMoeASRplmpCFkfMB60DUZx7oVjxNOqIH3UBR7AOd7j+9MfO0Hnqu8XgM+3pWmxz/0hoRds9asfDCMHnxmK0biQpBnRSGO0IBRzl0BmOjC/pLzPFONoas2Y+M5s2HlSPS4dsG5OckVL5Ii0mSP7JM8cgpKZJrUiYVwskTGZM38m49Ws/Wi/X6bU1ZyZtd8gvW5xeHCaXm</latexit><latexit sha1_base64="Igjn3htqGMa+w6xjh/e+ny+h0h0=">ACI3icfVBNS0JBFJ1nX2ZfVs2QxIYhLwXQW0CKYmWBvkBajJvOrkvA9m7gvk4c+pP5OrqKBF/6XR3qI0OovLufecgTnHDaXQaNsfVmphcWl5Jb2aWVvf2NzKbu9UdRApDhUeyEDVXaZBCh8qKFBCPVTAPFdCzR1cTvTaAygtAv8WhyG0PNbzRVdwhubUzhard3FTcyVCTCYOJdDSqB2L+9H5v2q+dHR12M7m7I9BZ0nTkJyJEG5nR03OwGPCRS6Z1w7FDbMVMoeASRplmpCFkfMB60DUZx7oVjxNOqIH3UBR7AOd7j+9MfO0Hnqu8XgM+3pWmxz/0hoRds9asfDCMHnxmK0biQpBnRSGO0IBRzl0BmOjC/pLzPFONoas2Y+M5s2HlSPS4dsG5OckVL5Ii0mSP7JM8cgpKZJrUiYVwskTGZM38m49Ws/Wi/X6bU1ZyZtd8gvW5xeHCaXm</latexit><latexit sha1_base64="Igjn3htqGMa+w6xjh/e+ny+h0h0=">ACI3icfVBNS0JBFJ1nX2ZfVs2QxIYhLwXQW0CKYmWBvkBajJvOrkvA9m7gvk4c+pP5OrqKBF/6XR3qI0OovLufecgTnHDaXQaNsfVmphcWl5Jb2aWVvf2NzKbu9UdRApDhUeyEDVXaZBCh8qKFBCPVTAPFdCzR1cTvTaAygtAv8WhyG0PNbzRVdwhubUzhard3FTcyVCTCYOJdDSqB2L+9H5v2q+dHR12M7m7I9BZ0nTkJyJEG5nR03OwGPCRS6Z1w7FDbMVMoeASRplmpCFkfMB60DUZx7oVjxNOqIH3UBR7AOd7j+9MfO0Hnqu8XgM+3pWmxz/0hoRds9asfDCMHnxmK0biQpBnRSGO0IBRzl0BmOjC/pLzPFONoas2Y+M5s2HlSPS4dsG5OckVL5Ii0mSP7JM8cgpKZJrUiYVwskTGZM38m49Ws/Wi/X6bU1ZyZtd8gvW5xeHCaXm</latexit><latexit sha1_base64="Igjn3htqGMa+w6xjh/e+ny+h0h0=">ACI3icfVBNS0JBFJ1nX2ZfVs2QxIYhLwXQW0CKYmWBvkBajJvOrkvA9m7gvk4c+pP5OrqKBF/6XR3qI0OovLufecgTnHDaXQaNsfVmphcWl5Jb2aWVvf2NzKbu9UdRApDhUeyEDVXaZBCh8qKFBCPVTAPFdCzR1cTvTaAygtAv8WhyG0PNbzRVdwhubUzhard3FTcyVCTCYOJdDSqB2L+9H5v2q+dHR12M7m7I9BZ0nTkJyJEG5nR03OwGPCRS6Z1w7FDbMVMoeASRplmpCFkfMB60DUZx7oVjxNOqIH3UBR7AOd7j+9MfO0Hnqu8XgM+3pWmxz/0hoRds9asfDCMHnxmK0biQpBnRSGO0IBRzl0BmOjC/pLzPFONoas2Y+M5s2HlSPS4dsG5OckVL5Ii0mSP7JM8cgpKZJrUiYVwskTGZM38m49Ws/Wi/X6bU1ZyZtd8gvW5xeHCaXm</latexit>Born terms
Formalism: Effective Chiral Lagrangian
16
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
V D
ij
= NiNj 12f 2 X
k
C(Born)
¯ ii,k
C(Born)
¯ jj,k
s − M 2
k
n (√s − Mk)(s + MiMj − √s(Mi + Mj))†s0
j s i
+(s + √s(Mi + Mj) + MiMj)(√s + Mk) (Ei + Mi)(Ej + Mj) †s0
j
[~ qj · ~ qi + i(~ qj × ~ qi) · ~ ] s
i
V C
ij
= −NiNj 12f 2 X
k
C(Born)
¯ jk,i
C(Born)
¯ ik,j
u − M 2
k
⇢ ⇥ u(√s + Mk) + √s(Mj(Mi + Mk) + MiMk) −Mj(Mi + Mk)(Mi + Mj) − M 2
i Mk
⇤ †s0
j s i +
⇥ u(√s − Mk) + √s(Mj(Mi + Mk) + MiMk) +Mj(Mi + Mk)(Mi + Mj) + M 2
i Mk
⇤ †s0
j
~ qj · ~ qi + i(~ qj × ~ qi) · ~
i
Formalism: Effective Chiral Lagrangian
17
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
L(2)
φB
= bDh ¯ B{χ+, B}i + bF h ¯ B[χ+, B]i + b0h ¯ BBihχ+i + d1h ¯ B{uµ, [uµ, B]}i +d2h ¯ B[uµ, [uµ, B]]i + d3h ¯ BuµihuµBi + d4h ¯ BBihuµuµi g1 8M 2
N
h ¯ B{uµ, [uν, {Dµ, Dν}B]}i g2 8M 2
N
h ¯ B[uµ, [uν, {Dµ, Dν}B]]i g3 8M 2
N
h ¯ Buµih[uν, {Dµ, Dν}B]i g4 8M 2
N
h ¯ B{Dµ, Dν}Bihuµuνi h1 4 h ¯ B[γµ, γν]Buµuνi h2 4 h ¯ B[γµ, γν]uµ[uν, B]i h3 4 h ¯ B[γµ, γν]uµ{uν, B}i h4 4 h ¯ B[γµ, γν]uµihuν, Bi + h.c.
<latexit sha1_base64="aREMGlDMmWAGHBUXH/pEFHOfgw=">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</latexit>be treated as parameters of the model! New terms taken into account
Formalism: Effective Chiral Lagrangian
18
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
V NLO
ij
= NiNj f 2 Dij − 2Lijqj
µqiµ +
1 2M 2
N
gij(pi
µqjµpi νqiν + pj µqjµpj νqiν)
✓ †s0
j s i
−†s0
j
~ qj · ~ qi + i(~ qj × ~ qi) · ~
i
◆ + NiNj f 2 hij − ✓ qj0qi2 Ei + Mi + qi0qj2 Ej + Mj + qj2qi2 (Ei + Mi)(Ej + Mj) + (~ qj · ~ qi)2 (Ei + Mi)(Ej + Mj) ◆ †s0
j s i
+ ✓ qi0 Ei + Mi + qj0 Ej + Mj ◆ †s0
j ~
qj · ~ qis
i +
✓ qi0 Ei + Mi + qj0 Ej + Mj + ~ qj · ~ qi (Ei + Mi)(Ej + Mj) − 1 ◆ i†s0
j (~
qj × ~ qi) · ~ s
i
Formalism: Effective Chiral Lagrangian
19
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
j [f(√s, ✓) − i(~
i
<latexit sha1_base64="NDQ16IgxWODrLXGc2KVYOPvUfc0=">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</latexit>Where:
∞
l=0
∞
l=1
Expansion in Legendre polynomials
Formalism: UChPT nonperturbative scheme
20
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
Unitarization: e.g. via the Bethe-Salpeter equation with on-shell amplitudes
à They should be separated in the Bethe-Salpeter equation and need to be redefined with a definite total angular momentum:
f tree
l+ (√s) =
1 2l + 1
j = l + 1
2
f tree
l− (√s) =
1 2l + 1
j = l − 1
2
<latexit sha1_base64="WYwq/MH2xptDzWOWaUX6CJfUng=">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</latexit>Finally, unitarized amplitudes …
l± G
l±
<latexit sha1_base64="halvmyUMaBk/Wr0mxz3MEqmSg=">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</latexit>Gl =
2Ml (4π)2
( al(µ)+ln M 2
l
µ2 + m2
l −M 2 l +s
2s
ln m2
l
M 2
l + qcm
√s ln
h
(s+2√sqcm)2−(M 2
l −m2 l )2
(s−2√sqcm)2−(M 2
l −m2 l )2
i )
<latexit sha1_base64="X7RX1hLi9XB3/Ml8DKHlyIN5XIM=">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</latexit><latexit sha1_base64="X7RX1hLi9XB3/Ml8DKHlyIN5XIM=">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</latexit><latexit sha1_base64="X7RX1hLi9XB3/Ml8DKHlyIN5XIM=">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</latexit><latexit sha1_base64="X7RX1hLi9XB3/Ml8DKHlyIN5XIM=">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</latexit>subtraction constants for the dimensional regularization scale ! = 1$%& in all the k channels.
Formalism: Fitting procedure
21
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
Fitting parameters:
partially constrained: 1.1234
567 ≤ 3 ≤ 1.26 34 567, 34 567=93 MeV
Formalism: Fitting procedure
22
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
Observable Points Observable Points σK−p→K−p 245 σK−p→ ¯
K0n
317 σK−p→π0Λ 225 σK−p→π0Σ0 125 σK−p→π−Σ+ 198 σK−p→π+Σ− 213 σK−p→ηΣ0 9 σK−p→ηΛ 106 σK−p→K+Ξ− 54 σK−p→K0Ξ0 30 γ 1 ∆E1s 1 Rn 1 Γ1s 1 Rc 1
<latexit sha1_base64="whpzy3YjBg242AZiT/fXqKPAcQ=">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</latexit>All available points for this energy range (1527 experimental points):
and Technology, Group I, Vol. 12, edited by H. Schopper (Springer, Berlin, 1988).
(2001).
σij = Mi Mj qj 4 π s qi ⇥ |f0|2 + 2|f1+|2 + |f1−|2 + 3|f2+|2 + 2|f2−|2⇤
<latexit sha1_base64="P6iuIwyU14TEUpZLQNcxsW9VLfs=">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</latexit>γ = Γ(Kp → π+Σ) Γ(Kp → πΣ+) = 2.36 ± 0.04 Rn = Γ(Kp → π0Λ) Γ(Kp → neutral states) = 0.664 ± 0.011 Rc = Γ(Kp → π+Σ, πΣ+) Γ(Kp → inelastic channels) = 0.189 ± 0.015
d.o.f =
k=1 nk
k=1 nk − p
K
k=1
k
Total cross section:
Branching ratios:
23
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
1600 1800 2000 2200 2400 2600 w [MeV] 50 100 150 200 σ(K
S+P waves S+P+D waves Former model (S-wave)
w [MeV] 1600 1800 2000 2200 2400 2600 w [MeV] 5 10 15 20 25 30 35 40 45 50 55 σ(K
0n) [mb]
1450 1500 1550 1600 1650 1700 w [MeV] 50 100 150 200 σ(K
S+P waves S+P+D waves Former model (S-wave)
55 w [MeV] 1450 1500 1550 1600 1650 1700 w [MeV] 5 10 15 20 25 30 35 40 45 50 55 σ(K
0n) [mb]
24
THEIA-STRONG2020 - Workshop 2019. November 25 - 29, 2019, Technik Museum Speyer.
Introduction: Theoretical Framework and Historical Background
25
STRANEX: Recent progress and perspectives in STRANge EXotic atoms studies and related topics. October 21 - 25, 2019, ECT* (Trento).
But it is not so straight forward … ! "# interaction is dominated by the presence of the $ %&'( resonance, located only 27 MeV below the Kbar-N threshold. à A nonperturbative resummation is needed!!!
(UChPT) in coupled channels. The pioneering work -- Kaiser, Siegel, Weise, NP A594 (1995) 325
Introduction: Theoretical Framework and Historical Background
26
STRANEX: Recent progress and perspectives in STRANge EXotic atoms studies and related topics. October 21 - 25, 2019, ECT* (Trento).
"# interaction with various degrees of sophistication: more channels, NLO Lagrangian, s-channel and u-channel Born terms…
V.K. Magas, E. Oset, A. Ramos, Phys. Rev. Lett. 95, 052301 (2005).
All of them obtaining in general similar features:
$% scattering data reproduced very satisfactorily
Motivation: Evolution of the model
27
STRANEX: Recent progress and perspectives in STRANge EXotic atoms studies and related topics. October 21 - 25, 2019, ECT* (Trento).
1440 1460 1480 1500
w [MeV]
30 60 90 120 150 σ(K
WT+Born+NLO WT+Born+NLO+RES
1440 1460 1480 1500
w [MeV]
10 20 30 40 50 60 σ(K
0n) [mb] WT+Born+NLO WT+Born+NLO+RES
1440 1460 1480 1500 10 20 30 40 50 60 σ(K
+) [mb]
1440 1460 1480 1500 50 100 150 200 σ(K
+Σ
1440 1460 1480 1500 20 40 60 80 σ(K
0Σ 0) [mb] WT+Born+NLO WT+Born+NLO+RES
1440 1460 1480 1500 10 20 30 40 σ(K
0Λ) [mb] WT+Born+NLO WT+Born+NLO+RES
1700 1800 1900 2000 2100 2200 0.5 1 1.5 2 σ(K
1700 1800 1900 2000 2100 2200 0.5 1 1.5 2 σ(K
0) [mb]
1800 2000 2200 2400 2600
w [MeV]
0.05 0.1 0.15 σ(K
0Ξ 0) [mb] WT+Born+NLO WT+Born+NLO+RES
1800 2000 2200 2400 2600
w [MeV]
0.05 0.1 0.15 0.2 0.25 σ(K
+Ξ
WT+Born+NLO WT+Born+NLO+RES
1660 1680 1700 0.5 1 1.5 2Total cross sections
Formalism: UChPT nonperturbative scheme Unitarization via the Bethe-Salpeter equation which it is solved by factorizing V and T matrices
28
2Ml (4π)2
l
µ2 + m2
l −M 2 l +s
2s
l
M 2
l + qcm
√s ln
(s+2√sqcm)2−(M 2
l −m2 l )2
(s−2√sqcm)2−(M 2
l −m2 l )2
subtraction constants for the dimensional regularization scale ! = #$%& in all the k channels. With isospin symmetry
Pure algebraic equation
aK−p = a ¯
K0n = a ¯ KN
aπ0Σ0 = aπ+Σ− = aπ−Σ+ = aπΣ aπΛ aηΣ aηΛ aK0Ξ0 = aK+Ξ− = aKΞ
<latexit sha1_base64="gZYwJ286CqFWakKlTM8r1zoiMY=">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</latexit><latexit sha1_base64="gZYwJ286CqFWakKlTM8r1zoiMY=">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</latexit><latexit sha1_base64="gZYwJ286CqFWakKlTM8r1zoiMY=">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</latexit><latexit sha1_base64="gZYwJ286CqFWakKlTM8r1zoiMY=">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</latexit> Introduction: Theoretical Framework and Historical Background
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STRANEX: Recent progress and perspectives in STRANge EXotic atoms studies and related topics. October 21 - 25, 2019, ECT* (Trento).
But it is not so straight forward … ! "# interaction is dominated by the presence of the $ %&'( resonance, located only 27 MeV below the Kbar-N threshold. à A nonperturbative resummation is needed!!! Back in 1950, Dalitz and Tuan already proposed that the ! K-N interaction is attractive enough to generate a quasi-bound state, the L(1405), below the "# threshold and embedded in the pS pS continuum.
Introduction: Theoretical Framework and Historical Background
30
STRANEX: Recent progress and perspectives in STRANge EXotic atoms studies and related topics. October 21 - 25, 2019, ECT* (Trento).
Magas, Oset, Ramos, PRL 95 (2005) 052301
All of them obtaining in general similar features:
"# scattering data reproduced very satisfactorily
− −
Motivation: Evolution of the model 1
31
STRANEX: Recent progress and perspectives in STRANge EXotic atoms studies and related topics. October 21 - 25, 2019, ECT* (Trento).
Special attention was paid to !"# → ! % reactions:
&'()⟶'+,+ = &'()⟶'.,( = 0
Assumption: the contribution of the Born diagrams would be very moderate. Next terms in hierarchy could play a relevant role in these channels!!! à New precision era requires a better knowledge of higher order corrections
Vij = V
W T
ij
+ V
NLO
ij
=⇒ T = (1 − V G)
−1V =⇒ Tij
<latexit sha1_base64="7TiTheW9VYIQLUdOyisi+yZE56I=">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</latexit><latexit sha1_base64="SWgvClIQvaA+DPqR470LyhgZ0=">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</latexit><latexit sha1_base64="SWgvClIQvaA+DPqR470LyhgZ0=">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</latexit><latexit sha1_base64="0DSxCgnESmWINDjZSYkzfJa5pt4=">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</latexit>Only S-wave contribution is taken into account
Motivation: Evolution of the model 1
32
STRANEX: Recent progress and perspectives in STRANge EXotic atoms studies and related topics. October 21 - 25, 2019, ECT* (Trento).
Experimental data employed in the fitting procedure
Results:
Motivation: Evolution of the model 2
33
STRANEX: Recent progress and perspectives in STRANge EXotic atoms studies and related topics. October 21 - 25, 2019, ECT* (Trento).
Vij = V
W T
ij
+ V
D
ij + V
C
ij + V
NLO
ij
= ⇒ T = (1 − V G)−1V = ⇒ Tij
<latexit sha1_base64="bSkfiuiUhTxMs2QWMKJA5u2ON/8=">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</latexit><latexit sha1_base64="xzWmobhVTRd9IUnI+1YIAkBblS4=">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</latexit><latexit sha1_base64="xzWmobhVTRd9IUnI+1YIAkBblS4=">ACyXicfZHNbhMxFIU9w0/L8BfKko1FhFRUGs2woZtKVYsEhEUKZlUyqSRx71JTD3jwb5DG8ysWPIaPA4vwAvwBuxZrKApvQsrOP7HVu+vmkhcEw/On5167fuLm2fiu4fefuvfutBxuxUaXm0OdKn2UMgNS5NBHgRKOCg0sSyUM0tODBR98Am2Eyns4L2CUsWkuJoIzdKVx6xe9WvHYig/VbnxsE8O1KHC54lwCHfSqGm9djl82NPgPrgav+2+awI06ap8qsV0hkxrdUaTZ7RHd+1mtB2/elod2+2oigO6EqtzQ3BuNUO2EtumqipWnvbf3+/g3axeG49SM5UbzMIEcumTHDKCxwZJlGwSVUQVIaKBg/ZVMYOpuzDMzI1vOo6JOJ0hRnQOv931nLMmPmWeoyGcOZucgWxcvYsMTJzsiKvCgRcu4ijk1KSVHRxVjpidDAUc6dYe4T3SspnzHNOLrhL9qPLja7auLnSjsRO/dP+yTRuvkEXlMNklEXpA98pockj7hXtfTnvW+G/8j/65/7mJ+t7yzEPyj/yvfwDvJtv0</latexit><latexit sha1_base64="TPj/nruKGTf8/fSjEUmyv/OFq98=">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</latexit>A new fit (with same set of experimental data) which includes the Born contributions was performed.
Results:
the goodness of this fit is comparable to that of Phys. Rev. C 92, 015206 (2015), but with very different parametrization: dissimilar NLO coefficients (unexpected compared to similar models in literature) more natural-sized subtraction constants (in accordance with similar models in literature) Only S-wave contribution is taken into account
Motivation: Evolution of the model 2
34
STRANEX: Recent progress and perspectives in STRANge EXotic atoms studies and related topics. October 21 - 25, 2019, ECT* (Trento).
The two models predict very different isospin contributions ➔ Isospin-filter observables are needed!
Formalism: Effective Chiral Lagrangian
MB = h ¯
MB(B, U) + L(2) MB(B, U)
<latexit sha1_base64="x656Dim2un4bE8RG7XfE6WXtEpA=">ACOXicbZDLSgMxFIYz9VbrbdSlm2ARWpQyUwTdCKVuXChUsBdoa8mkZ9rQzIUkI5ShT6aP4Au41JWoO1/AtJ1Fbfuv/vzfHzjnOCFnUlnWm5FaWV1b30hvZra2d3b3zP2DmgwiQaFKAx6IhkMkcOZDVTHFoREKIJ7Doe4Mrse8/gRCsB/UMQ2h7p+cxlCgdcwa1mp5RPUp4fHt6DEG1x3lymfV/NVMnOnEd7isac7OT+npUlpMaMfMWgVrIrxo7MRkUaJKx3xtdQMaeAryomUTdsKVTsmQjHKYZRpRJCQgekB01tfeKBbMeT/Uf4xA0EVn3Ak/dsNyaelEP0Z3xuHKejcNlrBkp97IdMz+MFPhUVzRzI45VgMdnxF0mgCo+1IZQwfSUmPaJIFTpY2f0+vb8soumVizYVsG+P8+Wyskh0ugIHaMcstEFKqEbVEFVRNEL+kDf6Md4Nt6NT+NrWk0ZyZ9D9E/G7x9rIqmG</latexit><latexit sha1_base64="x656Dim2un4bE8RG7XfE6WXtEpA=">ACOXicbZDLSgMxFIYz9VbrbdSlm2ARWpQyUwTdCKVuXChUsBdoa8mkZ9rQzIUkI5ShT6aP4Au41JWoO1/AtJ1Fbfuv/vzfHzjnOCFnUlnWm5FaWV1b30hvZra2d3b3zP2DmgwiQaFKAx6IhkMkcOZDVTHFoREKIJ7Doe4Mrse8/gRCsB/UMQ2h7p+cxlCgdcwa1mp5RPUp4fHt6DEG1x3lymfV/NVMnOnEd7isac7OT+npUlpMaMfMWgVrIrxo7MRkUaJKx3xtdQMaeAryomUTdsKVTsmQjHKYZRpRJCQgekB01tfeKBbMeT/Uf4xA0EVn3Ak/dsNyaelEP0Z3xuHKejcNlrBkp97IdMz+MFPhUVzRzI45VgMdnxF0mgCo+1IZQwfSUmPaJIFTpY2f0+vb8soumVizYVsG+P8+Wyskh0ugIHaMcstEFKqEbVEFVRNEL+kDf6Md4Nt6NT+NrWk0ZyZ9D9E/G7x9rIqmG</latexit><latexit sha1_base64="x656Dim2un4bE8RG7XfE6WXtEpA=">ACOXicbZDLSgMxFIYz9VbrbdSlm2ARWpQyUwTdCKVuXChUsBdoa8mkZ9rQzIUkI5ShT6aP4Au41JWoO1/AtJ1Fbfuv/vzfHzjnOCFnUlnWm5FaWV1b30hvZra2d3b3zP2DmgwiQaFKAx6IhkMkcOZDVTHFoREKIJ7Doe4Mrse8/gRCsB/UMQ2h7p+cxlCgdcwa1mp5RPUp4fHt6DEG1x3lymfV/NVMnOnEd7isac7OT+npUlpMaMfMWgVrIrxo7MRkUaJKx3xtdQMaeAryomUTdsKVTsmQjHKYZRpRJCQgekB01tfeKBbMeT/Uf4xA0EVn3Ak/dsNyaelEP0Z3xuHKejcNlrBkp97IdMz+MFPhUVzRzI45VgMdnxF0mgCo+1IZQwfSUmPaJIFTpY2f0+vb8soumVizYVsG+P8+Wyskh0ugIHaMcstEFKqEbVEFVRNEL+kDf6Md4Nt6NT+NrWk0ZyZ9D9E/G7x9rIqmG</latexit><latexit sha1_base64="x656Dim2un4bE8RG7XfE6WXtEpA=">ACOXicbZDLSgMxFIYz9VbrbdSlm2ARWpQyUwTdCKVuXChUsBdoa8mkZ9rQzIUkI5ShT6aP4Au41JWoO1/AtJ1Fbfuv/vzfHzjnOCFnUlnWm5FaWV1b30hvZra2d3b3zP2DmgwiQaFKAx6IhkMkcOZDVTHFoREKIJ7Doe4Mrse8/gRCsB/UMQ2h7p+cxlCgdcwa1mp5RPUp4fHt6DEG1x3lymfV/NVMnOnEd7isac7OT+npUlpMaMfMWgVrIrxo7MRkUaJKx3xtdQMaeAryomUTdsKVTsmQjHKYZRpRJCQgekB01tfeKBbMeT/Uf4xA0EVn3Ak/dsNyaelEP0Z3xuHKejcNlrBkp97IdMz+MFPhUVzRzI45VgMdnxF0mgCo+1IZQwfSUmPaJIFTpY2f0+vb8soumVizYVsG+P8+Wyskh0ugIHaMcstEFKqEbVEFVRNEL+kDf6Md4Nt6NT+NrWk0ZyZ9D9E/G7x9rIqmG</latexit>35
Motivation: Evolution of the model 3
36
STRANEX: Recent progress and perspectives in STRANge EXotic atoms studies and related topics. October 21 - 25, 2019, ECT* (Trento).
Prediction for Isospin filtering processes: !"
#$ ⟶ !&'# reaction (pure ( = 1 process)
1800 2000 2200 2400 2600 w [MeV] 0.05 0.1 0.15 0.2 0.25 σ (K
Lp ---> K +Ξ 0) [mb]
WT+NLO [31] WT+Born+NLO [32] WT+Born+NLO WT+Born+NLO+RES
1800 1950 2100 2250 2400 2550 MKΞ [MeV] 1 2 3 4 5 6 7 8 dΓ/dMKΞ [arb. units]
K
+Ξ
PS WT+Born+NLO ( x10 ) K
+Ξ
PS WT+NLO [31]
1650 1800 1950 2100 2250 2400 2550 MηΛ [MeV] 5 10 15 20 25 30 35 dΓ/dMηΛ [arb. units]
ηΛ WT+Born+NLO PS WT+Born+NLO ηΛ WT+NLO [31] PS WT+NLO [31]
Invariant mass distributions of !&'+ and ,- states in -. → 0/2 ,-, 0/2 !' decays J-Lab proposal for the secondary !" beam Data from LHCb would be very useful to constrain our models!
Formalism: Effective Chiral Lagrangian
Leff(B, U) = L(1)
MB(B, U) + L(2) MB(B, U)
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MB = h ¯
B(iγµDµ M0)Bi + 1 2Dh ¯ Bγµγ5{uµ, B}i + 1 2Fh ¯ Bγµγ5[uµ, B]i
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&'( ≤ ! ≤ 1.22 !% &'(, !% &'(=93 MeV.
V
W T
ij
= −Cij 1 4f 2 NiNj √s − Mi − Mj
37
Formalism: Effective Chiral Lagrangian
Leff(B, U) = L(1)
MB(B, U) + L(2) MB(B, U)
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MB = h ¯
B(iγµDµ M0)Bi + 1 2Dh ¯ Bγµγ5{uµ, B}i + 1 2Fh ¯ Bγµγ5[uµ, B]i
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D
ij = V
D
ij (D, F)
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ij = V
C
ij (D, F)
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Formalism: Effective Chiral Lagrangian
Leff(B, U) = L(1)
MB(B, U) + L(2) MB(B, U)
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MB = bDh ¯
B{χ+, B}i + bF h ¯ B[χ+, B]i + b0h ¯ BBihχ+i + d1h ¯ B{uµ, [uµ, B]}i+ d2h ¯ B[uµ, [uµ, B]]i + d3h ¯ BuµihuµBi + d4h ¯ BBihuµuµi
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NLO
ij
= 1 f 2 NiNj " Dij − 2 ωiωj + q2
i q2 j
3 (Mi + Ei) (Mj + Ej) ! Lij #
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<latexit sha1_base64="teiC3Eou13tLJf1N7en9dtfqf1A=">ACOXicbVBLSwMxEM7WV62vqkcvwSK0UMpuLehFKFrEg4cKthXaErLZtI3NPkiyQln6y/Qn+Ac86knUm3/AbLv4aJ0JM9/M9w1kxg4k8o0n4zUwuLS8kp6NbO2vrG5ld3eaUo/FIQ2iM9cWNjSTnzaEMxelNICh2bU5b9vAs5lt3VEjme9dqFNCui/se6zGClW6hbLOGInY7PpmvI3MIrRLQ7nBdgpfr/Yf+rL6dQ05R1kFaGDynE4LDqoUkDZnFkyJwbngZWAHEisjrKPHcnoUs9RTiWsm2ZgepGWChGOB1nOqGkASZD3KdtDT3sUtmNJvuP4UHPF1ANKJzUv7URdqUcubWuFgN5CwXN/j2qHqHXcj5gWhoh7REs31Qg6VD+MzQocJShQfaYCJYPqXkAywETpY2f0+tbsvOgWS5Zsm6quSqp8kh0mAP7IM8sMARqILUAcNQMADeAHv4MO4N56NV+NtKk0Zycwu+GPG5xdYq6Z3</latexit><latexit sha1_base64="teiC3Eou13tLJf1N7en9dtfqf1A=">ACOXicbVBLSwMxEM7WV62vqkcvwSK0UMpuLehFKFrEg4cKthXaErLZtI3NPkiyQln6y/Qn+Ac86knUm3/AbLv4aJ0JM9/M9w1kxg4k8o0n4zUwuLS8kp6NbO2vrG5ld3eaUo/FIQ2iM9cWNjSTnzaEMxelNICh2bU5b9vAs5lt3VEjme9dqFNCui/se6zGClW6hbLOGInY7PpmvI3MIrRLQ7nBdgpfr/Yf+rL6dQ05R1kFaGDynE4LDqoUkDZnFkyJwbngZWAHEisjrKPHcnoUs9RTiWsm2ZgepGWChGOB1nOqGkASZD3KdtDT3sUtmNJvuP4UHPF1ANKJzUv7URdqUcubWuFgN5CwXN/j2qHqHXcj5gWhoh7REs31Qg6VD+MzQocJShQfaYCJYPqXkAywETpY2f0+tbsvOgWS5Zsm6quSqp8kh0mAP7IM8sMARqILUAcNQMADeAHv4MO4N56NV+NtKk0Zycwu+GPG5xdYq6Z3</latexit><latexit sha1_base64="teiC3Eou13tLJf1N7en9dtfqf1A=">ACOXicbVBLSwMxEM7WV62vqkcvwSK0UMpuLehFKFrEg4cKthXaErLZtI3NPkiyQln6y/Qn+Ac86knUm3/AbLv4aJ0JM9/M9w1kxg4k8o0n4zUwuLS8kp6NbO2vrG5ld3eaUo/FIQ2iM9cWNjSTnzaEMxelNICh2bU5b9vAs5lt3VEjme9dqFNCui/se6zGClW6hbLOGInY7PpmvI3MIrRLQ7nBdgpfr/Yf+rL6dQ05R1kFaGDynE4LDqoUkDZnFkyJwbngZWAHEisjrKPHcnoUs9RTiWsm2ZgepGWChGOB1nOqGkASZD3KdtDT3sUtmNJvuP4UHPF1ANKJzUv7URdqUcubWuFgN5CwXN/j2qHqHXcj5gWhoh7REs31Qg6VD+MzQocJShQfaYCJYPqXkAywETpY2f0+tbsvOgWS5Zsm6quSqp8kh0mAP7IM8sMARqILUAcNQMADeAHv4MO4N56NV+NtKk0Zycwu+GPG5xdYq6Z3</latexit><latexit sha1_base64="teiC3Eou13tLJf1N7en9dtfqf1A=">ACOXicbVBLSwMxEM7WV62vqkcvwSK0UMpuLehFKFrEg4cKthXaErLZtI3NPkiyQln6y/Qn+Ac86knUm3/AbLv4aJ0JM9/M9w1kxg4k8o0n4zUwuLS8kp6NbO2vrG5ld3eaUo/FIQ2iM9cWNjSTnzaEMxelNICh2bU5b9vAs5lt3VEjme9dqFNCui/se6zGClW6hbLOGInY7PpmvI3MIrRLQ7nBdgpfr/Yf+rL6dQ05R1kFaGDynE4LDqoUkDZnFkyJwbngZWAHEisjrKPHcnoUs9RTiWsm2ZgepGWChGOB1nOqGkASZD3KdtDT3sUtmNJvuP4UHPF1ANKJzUv7URdqUcubWuFgN5CwXN/j2qHqHXcj5gWhoh7REs31Qg6VD+MzQocJShQfaYCJYPqXkAywETpY2f0+tbsvOgWS5Zsm6quSqp8kh0mAP7IM8sMARqILUAcNQMADeAHv4MO4N56NV+NtKk0Zycwu+GPG5xdYq6Z3</latexit>are not well established, so they should be treated as parameters of the model!
39
Formalism: Effective Chiral Lagrangian
Finally:
WT
ij
ij + VC ij + V
NLO
ij
−1V =⇒ Tij
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"#
$%, "&', "&(, ")', ")(, "$*
40
Goals and motivation
attention to the NLO coefficients, by fitting to the existing data.
γ = Γ(Kp → π+Σ) Γ(Kp → πΣ+) = 2.36 ± 0.04 Rn = Γ(Kp → π0Λ) Γ(Kp → neutral states) = 0.664 ± 0.011 Rc = Γ(Kp → π+Σ, πΣ+) Γ(Kp → inelastic channels) = 0.189 ± 0.015
Branching ratios: Energy shift and width of the kaonic hydrogen :
41
Isospin filtering processes: New Fits
Vij = V
W T
ij
+ V
D
ij + V
C
ij + V
NLO
ij
= ⇒ T = (1 − V G)−1V = ⇒ Tij
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Observable Points Observable Points σK−p→K−p 23 σK−p→ ¯
K0n
9 σK−p→π0Λ 3 σK−p→π0Σ0 3 σK−p→π−Σ+ 20 σK−p→π+Σ− 28 σK−p→ηΣ0 9 σK−p→ηΛ 49 σK−p→K+Ξ− 46 σK−p→K0Ξ0 29 γ 1 ∆E1s 1 Rn 1 Γ1s 1 Rc 1
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(WT+Born+NLO+RES)
a) Inclusion of high spin and high mass resonances allows us to study the stability of the NLO parameters (!", !$ , !%, &', &(, &), &*). b) It also simulates the contributions of higher angular momenta of the other channels via rescattering in the energy regime above +, threshold.
Sharov, Korotkikh, Lanskoy, EPJA 47 (2011) 109 Jackson, Oh, Haberzettl and Nakayama,Phys. Rev. C 91, 065208 (2015) Feijoo, Magas, Ramos, Phys. Rev. C 92, 015206 (2015)
Isospin filtering processes: Inclusion of Hyperonic resonances
T tot
ij
= T BS
ij
+ 1 p4MpMΞ X
JP
T JP
ij , JP = 3/2+, 5/2−, 7/2+
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ij
= T BS
ij
+ 1 p 4MpMΛ T 3/2+
ij
<latexit sha1_base64="rVNDH4algYW8Pr72qg0j9HQpMeM=">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</latexit><latexit sha1_base64="rVNDH4algYW8Pr72qg0j9HQpMeM=">ACMnicbVDNThsxGPQCpWFLIdAjF4sICYkq3aWR4IUpZceiACRAFI2WXkdLzHx/mB/ixRZfqv2LfoCwAkBNx4CJ6RSgX6n8cx8nzwT5YIr8LxrZ2Z27sP8x9KC+2nx89JyeWX1RGWFpKxNM5HJs4goJnjK2sBsLNcMpJEgp1Gwx9j/fSKScWztAWjnHUTcp7ymFMClgrLB61Q8wvT05CB2cOtnm4cmwkVfN0KYkmo9o0O1KUEXWuGeTM9u31PjHW8HdXf/+2bXpbxnXdsFzxqt5k8HvgT0EFTecwLP8J+hktEpYCFUSpju/l0NVEAqeCGTcoFMsJHZJz1rEwJQlTXT0JbvBGnEkMA4Yn73+9miRKjZLIehICA/VWG5P/0zoFxLtdzdO8AJZSa7FaXAgMGR73h/tcMgpiZAGhktfYjogtiewLY/j+2/Dvgcn21Xfq/pHtUq9MS2ihNbQOtpEPtpBdfQTHaI2oug3ukUP6NH5dw4d879i3XGme58Qa/GeXoG6tGqWQ=</latexit><latexit sha1_base64="rVNDH4algYW8Pr72qg0j9HQpMeM=">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</latexit><latexit sha1_base64="rVNDH4algYW8Pr72qg0j9HQpMeM=">ACMnicbVDNThsxGPQCpWFLIdAjF4sICYkq3aWR4IUpZceiACRAFI2WXkdLzHx/mB/ixRZfqv2LfoCwAkBNx4CJ6RSgX6n8cx8nzwT5YIr8LxrZ2Z27sP8x9KC+2nx89JyeWX1RGWFpKxNM5HJs4goJnjK2sBsLNcMpJEgp1Gwx9j/fSKScWztAWjnHUTcp7ymFMClgrLB61Q8wvT05CB2cOtnm4cmwkVfN0KYkmo9o0O1KUEXWuGeTM9u31PjHW8HdXf/+2bXpbxnXdsFzxqt5k8HvgT0EFTecwLP8J+hktEpYCFUSpju/l0NVEAqeCGTcoFMsJHZJz1rEwJQlTXT0JbvBGnEkMA4Yn73+9miRKjZLIehICA/VWG5P/0zoFxLtdzdO8AJZSa7FaXAgMGR73h/tcMgpiZAGhktfYjogtiewLY/j+2/Dvgcn21Xfq/pHtUq9MS2ihNbQOtpEPtpBdfQTHaI2oug3ukUP6NH5dw4d879i3XGme58Qa/GeXoG6tGqWQ=</latexit>Only for !"# ⟶ !% reactions: Only for !"# ⟶ &' reaction:
K )′+ , η )′+
p .+ Ξ .0+ , Λ .0+
23, 53 673!, 6'3& 6839
!
Y= ' :;<= , > ?=@= , > ??A= 9 !8 ⟶ 3 ⟶ !%, &'
' :;<= , BC = E
F G
L3/2±
BY K(q) = igBY3/2K
mK ¯ BΓ(±)Y µ
3/2∂µK + H.c.
T 3/2+
i j
(s0, s) = F3/2(k, k0) ¯ us0
j (p0)5k0 1S 3/2(q)k25us i (p) ,
> ?=@= , BC = H
F G
L5/2±
BY K(q) = igBY5/2K
m2
K
¯ BΓ(±)Y µν
5/2∂µ∂νK + H.c.
> ??A= , BC = I
F "
L7/2±
BY K(q) = −gBY7/2K
m3
K
¯ BΓ(⌥)Y µνα
7/2 ∂µ∂ν∂αK + H.c.
T 5/2
i j
(s0, s) = F5/2(k, k0) ¯ us0
j (p0)k0 1k0 2S 5/2(q)k↵1k↵2us i (p) ,
T 7/2+
ij
(s0, s) = F7/2(k, k0) ¯ us0
j (p0)k0 β1k0 β2k0 β3S7/2(q)kα1kα2kα3us i (p)
FJ(k, k0) = gBYJMgNYJ ¯
K
m2J1
K
exp ⇣ ~ k2/Λ2
J
⌘ exp ✓ ~ k02/Λ2
J
◆
FORM FACTORS Sharov, Korotkikh, Lanskoy, EPJA 47 (2011) 109
Isospin filtering processes: Results Total cross sections:
Isospin filtering processes: Results Fitting parameters:
Very homogeneous and accurate values Naturally sized values for all 16% improvement on the goodness of the fit
WT+Born+NLO WT+NLO+Born+RES a ¯
KN (10−3)
1.268+0.096
−0.096
1.517 ± 0.208 aπΛ (10−3) −6.114+0.045
−0.055
−2.624 ± 13.926 aπΣ (10−3) 0.684+0.429
−0.572
2.146 ± 1.174 aηΛ (10−3) −0.666+0.080
−0.140
0.756 ± 1.215 aηΣ (10−3) 8.004+2.282
−0.978
10.105 ± 3.660 aKΞ (10−3) −2.508+0.396
−0.297
−2.013 ± 0.743 f/fπ 1.196+0.013
−0.007
1.180 ± 0.028 b0 (GeV −1) 0.129+0.032
−0.032
−0.071 ± 0.016 bD (GeV −1) 0.120+0.010
−0.009
0.128 ± 0.015 bF (GeV −1) 0.209+0.022
−0.026
0.271 ± 0.022 d1 (GeV −1) 0.151+0.021
−0.027
0.144 ± 0.034 d2 (GeV −1) 0.126+0.012
−0.009
0.133 ± 0.011 d3 (GeV −1) 0.299+0.020
−0.024
0.405 ± 0.022 d4 (GeV −1) 0.249+0.027
−0.033
0.022 ± 0.020 D 0.700+0.064
−0.144
0.700 ± 0.148 F 0.510+0.060
−0.050
0.400 ± 0.110 gΛY3/2η · gNY3/2 ¯
K
gΞY3/2K · gNY3/2 ¯
K
gΞY5/2K · gNY5/2 ¯
K
gΞY7/2K · gNY7/2 ¯
K
Λ3/2 (MeV)
Λ5/2 (MeV)
Λ7/2 (MeV)
MY3/2 (MeV)
MY5/2 (MeV)
MY7/2 (MeV)
Γ3/2 (MeV)
Γ5/2 (MeV)
Γ7/2 (MeV)
χ2
d.o.f.
1.14 0.96
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Isospin filtering processes
46
Scenarios consisting of processes which filter isospin could provide more constraints in
pure % = $ and % = ' processes respectively. Until now the scattering data used in the fits come from:
$* ⟶ (,-$, pure % = '
process.
K−p → π−Σ+, π0Σ0, π+Σ−, ¯ K0n, K−p, π0Λ, K0Ξ0, K+Ξ−
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47
Prediction for !"
#$ ⟶ !&'# reaction (pure ( = 1 process):
Isospin filtering processes
48
Scenarios consisting of processes which filter isospin could provide more constraints in
pure % = $ and % = ' processes respectively. Until now the scattering data used in the fits come from:
$* ⟶ (,-$, pure % = '
process.
K−p → π−Σ+, π0Σ0, π+Σ−, ¯ K0n, K−p, π0Λ, K0Ξ0, K+Ξ−
<latexit sha1_base64="9ao6PUk6XoWeZpgAyrUquavfwnI=">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</latexit><latexit sha1_base64="9ao6PUk6XoWeZpgAyrUquavfwnI=">ACWXicdVHbSgMxEM2ut7reqn30JVgEwbZkRdDHoi9CfVC0Wui2ZTbNtqHZC0lWKEv/0B8Q/Riz6wpe5yXnzDkzmUz8RHClCXmx7KXldW1yrqzsbm1vVPd3XtQcSop69JYxLng2KCR6yruRasl0gGoS/Yoz+7zPXHJyYVj6N7PU/YIRJxANOQZvUqPrUGTZxgj0dYy/hw6Z3xychDI8bBSW45OSDH5e0agPMusjCVqFD0aZcG1uXwMxhCnvpB1hkSr8fzDh1Tb1Bz4Tijap20Tke+DdwW8VJ6qiMm1H12RvHNA1ZpKkApfouSfQgA6k5FWzheKliCdAZTFjfwAhCpgZsZ8FPgxifWU4YJ/9WYQKjUPfePJx1U/tTz5l9ZPdXA+yHiUpJpF1FiMFqQCmz3ma8ZjLhnVYm4AUMnNlJhOQLV5jPy53+Ef8PHk5aLm5t6f19kW5iAraRwfoCLnoDLXRFbpBXUTRm2VbG9am9WpbdsV2Pqy2VdbU0Lewa+83V61C</latexit><latexit sha1_base64="9ao6PUk6XoWeZpgAyrUquavfwnI=">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</latexit><latexit sha1_base64="9ao6PUk6XoWeZpgAyrUquavfwnI=">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</latexit>Roca, Mai, Oset and Meissner, Eur. Phys. J. C 75, no. 5, 218 (2015).
Production mechanism of a meson-baryon pair from the !" weak decay
b u d c ¯ c W s ¯ uu + ¯ dd + ¯ ss u d Weak decay Hadronization
#/% &' Weak decay
Roca, Mai, Oset and Meissner, Eur. Phys. J. C 75, no. 5, 218 (2015)
| ⟩ !" =
1 |
⟩ 2 34 − 43 1 2 | ⟩ 8 34 − 43
Cabibbo favored weak transition
49
Production mechanism of a meson-baryon pair from the !" weak decay 1 2 | ⟩ ' () − )( 1 2 + , ' - (( + ̅ )) + ̅ '' () − )( = |12 ⟩ 3 + |4 15 ⟩ 6 + 2 3 |8 ⟩ Λ |1∗2 ⟩ 3 + |4 1∗5 ⟩ 6 − 2 3 | ⟩ ;Λ
(=> ) (@> ) A= = B/D2, F/D2
b u d c ¯ c W s ¯ uu + ¯ dd + ¯ ss u d Weak decay Hadronization
A/G M> HI Weak decay Hadronizatio n =>, , pseudoscalar-baryon @>, vector-baryon
50
Production mechanism of a meson-baryon pair from the !" weak decay
b u d c ¯ c W s ¯ uu + ¯ dd + ¯ ss u d Weak decay Hadronization
%/' M( #$ Weak decay Hadronizatio n ) = 0 ) = 0 ) = 0
51
!" → $/& '!, $/& () decays: Transition amplitude
Unknown overall factor Arbitrary units Taken as a constant value
Feijoo, Magas, Ramos, Oset: Phys.Rev. D92 (2015) no.7, 076015, Erratum: Phys.Rev. D95 (2017) no.3, 039905
52
M(MMB, MJ/ψB) = Vp h hMB + X
i
hiGi(MMB)ti,φB(MMB) i
<latexit sha1_base64="2Hk5BW/vOMQ8vGfzk4dvtFX04Jo=">ACVHicbVFbS8MwGE3rfd6mPvry4RAmymxF0BdhzAdFGCi4KaylpDFbg2kbk1QYpf/QZ8X/omC69cHb95LznQskJ6HgTGnHebfsmdm5+YXFpdryuraen1js6/STBLaIylP5X2IFeUsoT3NKf3QlIch5zehY/npX73TKViaXKrx4L6MR4lbMgI1oYK6k9ejHVEM+7RbMb5F3oFAfmvDr0hGJm2YMz6Ae5KMDrsNEAoqkH9sFTWRwQzC4CFgTqvQe6CBnB56Iyvg3usz7tVpQbzgtZzLwF7gVaKBqroP6i/eQkiymiSYcKzVwHaH9HEvNCKdFzcsUFZg84hEdGJjgmCo/n1RTwO4wlaAjCpP9uzfHsVLjODSesgL1WyvJ/7RBpoenfs4SkWmaEGMx2jDjoFMoG4YHJinRfGwAJpKZWwKJsMREm38on+/+fuxf0D9quU7LvTlutDtVEYtoG+2gJnLRCWqjS3SNeoigN/RpzVsL1qv1Yc/Yc1OrbVWZLfRj7LUvNEetmw=</latexit><latexit sha1_base64="2Hk5BW/vOMQ8vGfzk4dvtFX04Jo=">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</latexit><latexit sha1_base64="2Hk5BW/vOMQ8vGfzk4dvtFX04Jo=">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</latexit><latexit sha1_base64="2Hk5BW/vOMQ8vGfzk4dvtFX04Jo=">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</latexit> !" → $/& '!, $/& () decays: Transition amplitude
53
M(MMB, MJ/ψB) = Vp h hMB + X
i
hiGi(MMB)ti,φB(MMB) i
<latexit sha1_base64="2Hk5BW/vOMQ8vGfzk4dvtFX04Jo=">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</latexit><latexit sha1_base64="2Hk5BW/vOMQ8vGfzk4dvtFX04Jo=">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</latexit><latexit sha1_base64="2Hk5BW/vOMQ8vGfzk4dvtFX04Jo=">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</latexit><latexit sha1_base64="2Hk5BW/vOMQ8vGfzk4dvtFX04Jo=">ACVHicbVFbS8MwGE3rfd6mPvry4RAmymxF0BdhzAdFGCi4KaylpDFbg2kbk1QYpf/QZ8X/omC69cHb95LznQskJ6HgTGnHebfsmdm5+YXFpdryuraen1js6/STBLaIylP5X2IFeUsoT3NKf3QlIch5zehY/npX73TKViaXKrx4L6MR4lbMgI1oYK6k9ejHVEM+7RbMb5F3oFAfmvDr0hGJm2YMz6Ae5KMDrsNEAoqkH9sFTWRwQzC4CFgTqvQe6CBnB56Iyvg3usz7tVpQbzgtZzLwF7gVaKBqroP6i/eQkiymiSYcKzVwHaH9HEvNCKdFzcsUFZg84hEdGJjgmCo/n1RTwO4wlaAjCpP9uzfHsVLjODSesgL1WyvJ/7RBpoenfs4SkWmaEGMx2jDjoFMoG4YHJinRfGwAJpKZWwKJsMREm38on+/+fuxf0D9quU7LvTlutDtVEYtoG+2gJnLRCWqjS3SNeoigN/RpzVsL1qv1Yc/Yc1OrbVWZLfRj7LUvNEetmw=</latexit>hπ0Σ0 = hπ+Σ− = hπ−Σ+ = hK+Ξ− = hK0Ξ0 = 0 , hK−p = h ¯
K0n = 1 , hηΛ = − √ 2 3
!" → $/& '!, $/& () decays: Transition amplitude
54
M(MMB, MJ/ψB) = Vp h hMB + X
i
hiGi(MMB)ti,φB(MMB) i
<latexit sha1_base64="2Hk5BW/vOMQ8vGfzk4dvtFX04Jo=">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</latexit><latexit sha1_base64="2Hk5BW/vOMQ8vGfzk4dvtFX04Jo=">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</latexit><latexit sha1_base64="2Hk5BW/vOMQ8vGfzk4dvtFX04Jo=">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</latexit><latexit sha1_base64="2Hk5BW/vOMQ8vGfzk4dvtFX04Jo=">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</latexit>(12, '!)
Gl = 2Ml (4⇡)2 ( al(µ) + ln M 2
l
µ2 + m2
l − M 2 l + s
2s ln m2
l
M 2
l
+ qcm √s ln (s + 2√sqcm)2 − (M 2
l − m2 l )2
(s − 2√sqcm)2 − (M 2
l − m2 l )2
) .
WT+NLO Phys. Rev. C 92, 015206 (2015) WT+Born+NLO new fit
!" → $/& '!, $/& () decays : double differential cross-section and predictions
Fixing the invariant mass *+, and integrating over *
55
Λb
1800 1950 2100 2250 2400 2550 MKΞ [MeV] 1 2 3 4 5 6 7 8 dΓ/dMKΞ [arb. units]
K
+Ξ
PS WT+Born+NLO ( x10 ) K
+Ξ
PS WT+NLO [30]
1650 1800 1950 2100 2250 2400 2550 MηΛ [MeV] 5 10 15 20 25 30 35 dΓ/dMηΛ [arb. units]
ηΛ WT+Born+NLO PS WT+Born+NLO ηΛ WT+NLO [30] PS WT+NLO [30]
Promising data from LHCb would be very useful to constrain our models!
CONCLUSIONS
technique to describe low energy hadron dynamics.
"# ⟶ "% channels are very sensitive to the NLO terms of the lagrangian as well as to the Born terms, so they provide more reliable values of the NLO parameters.
"# interaction that fit the scattering data equally well have very different isospin decomposition. Therefore, experimental data from processes which filter isospin have been shown to be very helpful to reproduce properly the whole meson-baryon channels of the S=-1 sector and to constrain the fitting parameters. "&
'( ⟶ ")%'(J-Lab)
*+⟶ ,/. /*, ,/. "% (LHCb?)
! "# ⟶ "%, /* reactions giving a significantly better agreement with experimental data. Their inclusion is also a helpful tool to study the stability of the NLO parameters.
56
WT+Born+NLO Considering !"# ⟶ %&, %'( scattering data in the fit
1700 1800 1900 2000 2100 2200
w [MeV]
0,5 1 1,5 2
σ(K
WT+NLO WT+NLO+Born WT+NLO+Born (η chan) 1700 1800 1900 2000 2100 2200
w [MeV]
0,5 1 1,5 2
σ(K
0) [mb]
WT+NLO WT+NLO+Born WT+NLO+Born (η chan) 1800 2000 2200 2400 2600
w [MeV]
0,03 0,06 0,09 0,12 0,15
σ(K
0Ξ 0) [mb]
1800 2000 2200 2400 2600
w [MeV]
0,05 0,1 0,15 0,2 0,25
σ(K
+Ξ
24
57
CONCLUSIONS
58
powerful technique to describe low energy hadron dynamics.
"# ⟶ "% channels are very sensitive to the NLO terms of the lagrangian as well as to the Born terms, so they provide more reliable values of the NLO parameters.
"# interaction that fit the scattering data equally well have very different isospin decomposition. Therefore, experimental data from processes which filter isospin have been shown to be very helpful to reproduce properly the whole meson-baryon channels of the S=-1 sector and to constrain the fitting parameters. "&
'( ⟶ ")%'(J-Lab)
*+⟶ ,/. /*, ,/. "% (LHCb?)
in the ! "# ⟶ "%, /* reactions giving a significantly better agreement with experimental data.