Pub Date : 2021-12-31DOI: 10.5506/APhysPolB.54.6-A2
Florian Nortier
Particle physics models with extra dimensions of space (EDS's) and branes shed new light on electroweak and flavor hierarchies with a rich TeV scale phenomenology. This article highlights new model building issues with EDS's and branes, arising in the framework of weakly nonlocal field theories. It is shown that a brane-localized field is still delocalized in the bulk on a small distance from the brane position: fields localized on such distant fuzzy branes are thus allowed to interact directly with suppressed couplings. Directions for model building are also given: (i) with fuzzy branes, a new realization of split fermions in an EDS is presented, naturally generating flavor hierarchies; (ii) with a warped EDS, the usual warp transmutation of a brane-localized mass term is revisited, where it is shown that the nonlocal scale is also redshifted and provides a smooth UV cutoff for the Higgs boson mass. This framework is expected to have natural UV completions in string theory, but the possibility to embed it in recent UV complete weakly nonlocal quantum field theories is commented.
{"title":"Extra Dimensions and Fuzzy Branes in String-inspired Nonlocal Field Theory","authors":"Florian Nortier","doi":"10.5506/APhysPolB.54.6-A2","DOIUrl":"https://doi.org/10.5506/APhysPolB.54.6-A2","url":null,"abstract":"Particle physics models with extra dimensions of space (EDS's) and branes shed new light on electroweak and flavor hierarchies with a rich TeV scale phenomenology. This article highlights new model building issues with EDS's and branes, arising in the framework of weakly nonlocal field theories. It is shown that a brane-localized field is still delocalized in the bulk on a small distance from the brane position: fields localized on such distant fuzzy branes are thus allowed to interact directly with suppressed couplings. Directions for model building are also given: (i) with fuzzy branes, a new realization of split fermions in an EDS is presented, naturally generating flavor hierarchies; (ii) with a warped EDS, the usual warp transmutation of a brane-localized mass term is revisited, where it is shown that the nonlocal scale is also redshifted and provides a smooth UV cutoff for the Higgs boson mass. This framework is expected to have natural UV completions in string theory, but the possibility to embed it in recent UV complete weakly nonlocal quantum field theories is commented.","PeriodicalId":7060,"journal":{"name":"Acta Physica Polonica B","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46598040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-29DOI: 10.5506/aphyspolb.53.1-a3
P. Chankowski, J. Wojtkiewicz
We report the results of the computation of the order ( k F a 0 ) 2 correction, where k F = 3 π 2 ρ is the Fermi wave vector and a 0 the s -wave scattering length of the repulsive interaction, to the ground-state energy of a mixture of oppositely polarized N a spin 1 / 2 fermions a of masses m a and N b spin 1 / 2 fermions b of masses m b ( ρ = N/V , N = N a + N b ). It is shown that the results of the paper [1] in which the same correction has been computed entirely numerically, using a more traditional approach, can be easily and semianalytically reproduced using the effective field theory technique.
我们报告的结果计算的顺序(k F(0) 2校正,其中2 k F = 3πρ是费米波矢和0 s波散射长度的排斥作用,面对面的混合物的基态能量极化N自旋1 / 2费米子质量m和N b旋转1 / 2费米子质量m b(ρ= N / V, N = N + N b)。结果表明，采用更传统的方法完全用数值方法计算相同的修正量，可以很容易地用有效场论技术半解析地再现。
{"title":"On the Ground-state Energy of a Mixture of Two Different Oppositely Polarized Fermionic Gases","authors":"P. Chankowski, J. Wojtkiewicz","doi":"10.5506/aphyspolb.53.1-a3","DOIUrl":"https://doi.org/10.5506/aphyspolb.53.1-a3","url":null,"abstract":"We report the results of the computation of the order ( k F a 0 ) 2 correction, where k F = 3 π 2 ρ is the Fermi wave vector and a 0 the s -wave scattering length of the repulsive interaction, to the ground-state energy of a mixture of oppositely polarized N a spin 1 / 2 fermions a of masses m a and N b spin 1 / 2 fermions b of masses m b ( ρ = N/V , N = N a + N b ). It is shown that the results of the paper [1] in which the same correction has been computed entirely numerically, using a more traditional approach, can be easily and semianalytically reproduced using the effective field theory technique.","PeriodicalId":7060,"journal":{"name":"Acta Physica Polonica B","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44821422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-10DOI: 10.5506/APhysPolB.52.1357
W. A. Yahya, K. Oyewumi
The calculations of the alpha decay half-lives of some Polonium isotopes in the mass range 186 - 218 have been carried out using the Wentzel-Kramers-Brillouin (WKB) semiclassical approximation. The alpha-nucleus effective potential used contains the Coulomb potential, centrifugal potential, and the nuclear potential. The nuclear potential is obtained via the double folding model, with the microscopic NN effective interactions derived from relativistic mean field theory Lagrangian (termed R3Y). Different parametrizations of the R3Y interactions have been employed in the computation of the nuclear potentials. The results obtained using the R3Y NN interactions are compared with the ones obtained using the famous Michigan-3-Yukawa (M3Y) interactions. The use of density-dependent NN interaction is also considered. When compared to available experimental data, there are improvements in the results when density-dependent interaction potentials are used compared to when density-independent interactions are employed.
{"title":"Calculations of the Alpha Decay Half-lives of Some Polonium Isotopes Using the Double Folding Model","authors":"W. A. Yahya, K. Oyewumi","doi":"10.5506/APhysPolB.52.1357","DOIUrl":"https://doi.org/10.5506/APhysPolB.52.1357","url":null,"abstract":"The calculations of the alpha decay half-lives of some Polonium isotopes in the mass range 186 - 218 have been carried out using the Wentzel-Kramers-Brillouin (WKB) semiclassical approximation. The alpha-nucleus effective potential used contains the Coulomb potential, centrifugal potential, and the nuclear potential. The nuclear potential is obtained via the double folding model, with the microscopic NN effective interactions derived from relativistic mean field theory Lagrangian (termed R3Y). Different parametrizations of the R3Y interactions have been employed in the computation of the nuclear potentials. The results obtained using the R3Y NN interactions are compared with the ones obtained using the famous Michigan-3-Yukawa (M3Y) interactions. The use of density-dependent NN interaction is also considered. When compared to available experimental data, there are improvements in the results when density-dependent interaction potentials are used compared to when density-independent interactions are employed.","PeriodicalId":7060,"journal":{"name":"Acta Physica Polonica B","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46608873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-05DOI: 10.5506/APhysPolB.53.7-A3
M. Je.zabek, A. Rybicki
We apply our recently formulated Gluon Exchange Model (GEM) to baryon production in proton-nucleus reactions involving N>1 proton-nucleon collisions. We propose a description scheme for the process of soft color octet (gluon) exchange, based on the assumption that probabilities to form an effective diquark are equal for all allowed pairs of quarks. The latter effective diquark can form either from two valence, one valence and one sea, or from two sea quarks. Consequently we calculate the probabilities for different color configurations involving diquarks of valence-valence, valence-sea and sea-sea type. These probabilities appear to depend on the number of exchanged gluons, which results in increasing baryon stopping as a function of the number of proton-nucleon collisions in the nucleus. As such, the nuclear stopping power appears to be governed by the emergence of new color configurations as a function of N rather than by the energy loss of the original valence diquark. The advantage of our approach lies in its high predictive power which makes it verifiable by the new, precise data on proton and neutron production from the CERN SPS. The latter verification, and a set of predictions for the N-dependence of the baryon stopping process, are included in the letter.
{"title":"The Gluon Exchange Model in Proton–Nucleus Collisions","authors":"M. Je.zabek, A. Rybicki","doi":"10.5506/APhysPolB.53.7-A3","DOIUrl":"https://doi.org/10.5506/APhysPolB.53.7-A3","url":null,"abstract":"We apply our recently formulated Gluon Exchange Model (GEM) to baryon production in proton-nucleus reactions involving N>1 proton-nucleon collisions. We propose a description scheme for the process of soft color octet (gluon) exchange, based on the assumption that probabilities to form an effective diquark are equal for all allowed pairs of quarks. The latter effective diquark can form either from two valence, one valence and one sea, or from two sea quarks. Consequently we calculate the probabilities for different color configurations involving diquarks of valence-valence, valence-sea and sea-sea type. These probabilities appear to depend on the number of exchanged gluons, which results in increasing baryon stopping as a function of the number of proton-nucleon collisions in the nucleus. As such, the nuclear stopping power appears to be governed by the emergence of new color configurations as a function of N rather than by the energy loss of the original valence diquark. The advantage of our approach lies in its high predictive power which makes it verifiable by the new, precise data on proton and neutron production from the CERN SPS. The latter verification, and a set of predictions for the N-dependence of the baryon stopping process, are included in the letter.","PeriodicalId":7060,"journal":{"name":"Acta Physica Polonica B","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44223319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-28DOI: 10.5506/aphyspolb.53.1-a5
F. Klinkhamer
A direct algebraic solution has been obtained from the full bosonic master-field equation of the IIB matrix model for low dimensionality D = 3 and small matrix size N = 3. A different method is needed for larger values of D and N . Here, we explore an indirect numerical approach and obtain an approximate numerical solution for the nontrivial case (D, N) = (10, 4) with a complex Pfaffian. We also present a suggestion for numerical calculations at larger values of N . Acta Phys. Pol. B arXiv:2110.15309 (v4)
{"title":"Towards a Numerical Solution of the Bosonic Master-Field Equation of the IIB Matrix Model","authors":"F. Klinkhamer","doi":"10.5506/aphyspolb.53.1-a5","DOIUrl":"https://doi.org/10.5506/aphyspolb.53.1-a5","url":null,"abstract":"A direct algebraic solution has been obtained from the full bosonic master-field equation of the IIB matrix model for low dimensionality D = 3 and small matrix size N = 3. A different method is needed for larger values of D and N . Here, we explore an indirect numerical approach and obtain an approximate numerical solution for the nontrivial case (D, N) = (10, 4) with a complex Pfaffian. We also present a suggestion for numerical calculations at larger values of N . Acta Phys. Pol. B arXiv:2110.15309 (v4)","PeriodicalId":7060,"journal":{"name":"Acta Physica Polonica B","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70739723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-22DOI: 10.5506/aphyspolb.53.6-a1
A. Buras, E. Venturini
We reemphasize the strong dependence of the branching ratios $B(K^+topi^+nubarnu)$ and $B(K_Ltopi^0nubarnu)$ on $|V_{cb}|$ that is stronger than in rare $B$ decays, in particular for $K_Ltopi^0nubarnu$. Thereby the persistent tension between inclusive and exclusive determinations of $|V_{cb}|$ weakens the power of these theoretically clean decays in the search for new physics (NP). We demonstrate how this uncertainty can be practically removed by considering within the SM suitable ratios of the two branching ratios between each other and with other observables like the branching ratios for $K_Stomu^+mu^-$, $B_{s,d}tomu^+mu^-$ and $Bto K(K^*)nubarnu$. We use as basic CKM parameters $V_{us}$, $|V_{cb}|$ and the angles $beta$ and $gamma$ in the unitarity triangle (UT). This avoids the use of the problematic $|V_{ub}|$. A ratio involving $B(K^+topi^+nubarnu)$ and $B(B_stomu^+mu^-)$ while being $|V_{cb}|$-independent exhibits sizable dependence on the angle $gamma$. It should be of interest for several experimental groups in the coming years. We point out that the $|V_{cb}|$-independent ratio of $B(B^+to K^+nubarnu)$ and $B(B_stomu^+mu^-)$ from Belle II and LHCb signals a $1.8sigma$ tension with its SM value. As a complementary test of the Standard Model, we propose to extract $|V_{cb}|$ from different observables as a function of $beta$ and $gamma$. We illustrate this with $epsilon_K$, $Delta M_d$ and $Delta M_s$ finding tensions between these three determinations of $|V_{cb}|$ within the SM. From $Delta M_s$ and $S_{psi K_S}$ alone we find $|V_{cb}|=41.8(6)times 10^{-3}$ and $|V_{ub}|=3.65(12)times 10^{-3}$. We stress the importance of a precise measurement of $gamma$. We obtain most precise SM predictions for considered branching ratios of rare K and B decays to date.
{"title":"Searching for New Physics in Rare (K) and (B) Decays without (|V_{cb}|) and (|V_{ub}|) Uncertainties","authors":"A. Buras, E. Venturini","doi":"10.5506/aphyspolb.53.6-a1","DOIUrl":"https://doi.org/10.5506/aphyspolb.53.6-a1","url":null,"abstract":"We reemphasize the strong dependence of the branching ratios $B(K^+topi^+nubarnu)$ and $B(K_Ltopi^0nubarnu)$ on $|V_{cb}|$ that is stronger than in rare $B$ decays, in particular for $K_Ltopi^0nubarnu$. Thereby the persistent tension between inclusive and exclusive determinations of $|V_{cb}|$ weakens the power of these theoretically clean decays in the search for new physics (NP). We demonstrate how this uncertainty can be practically removed by considering within the SM suitable ratios of the two branching ratios between each other and with other observables like the branching ratios for $K_Stomu^+mu^-$, $B_{s,d}tomu^+mu^-$ and $Bto K(K^*)nubarnu$. We use as basic CKM parameters $V_{us}$, $|V_{cb}|$ and the angles $beta$ and $gamma$ in the unitarity triangle (UT). This avoids the use of the problematic $|V_{ub}|$. A ratio involving $B(K^+topi^+nubarnu)$ and $B(B_stomu^+mu^-)$ while being $|V_{cb}|$-independent exhibits sizable dependence on the angle $gamma$. It should be of interest for several experimental groups in the coming years. We point out that the $|V_{cb}|$-independent ratio of $B(B^+to K^+nubarnu)$ and $B(B_stomu^+mu^-)$ from Belle II and LHCb signals a $1.8sigma$ tension with its SM value. As a complementary test of the Standard Model, we propose to extract $|V_{cb}|$ from different observables as a function of $beta$ and $gamma$. We illustrate this with $epsilon_K$, $Delta M_d$ and $Delta M_s$ finding tensions between these three determinations of $|V_{cb}|$ within the SM. From $Delta M_s$ and $S_{psi K_S}$ alone we find $|V_{cb}|=41.8(6)times 10^{-3}$ and $|V_{ub}|=3.65(12)times 10^{-3}$. We stress the importance of a precise measurement of $gamma$. We obtain most precise SM predictions for considered branching ratios of rare K and B decays to date.","PeriodicalId":7060,"journal":{"name":"Acta Physica Polonica B","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43635388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-30DOI: 10.5506/APhysPolB.51.561
P. Thirolf, B. Seiferle, L. Wense, I. Amersdorffer, D. Moritz, J. Weitenberg
Given the drastic progress achieved during recent years in our knowledge on the decay and nuclear properties of the thorium isomer Th, the focus of research on this potential nuclear clock transition will turn in the near future from the nuclear physics driven ‘search and characterization phase’ towards a laser physics driven ‘consolidation and realization phase’. This prepares the path towards the ultimate goal of the realization of a nuclear frequency standard, the ‘Nuclear Clock’. This article briefly summarizes our present knowledge, focusing on recent achievements, and points to the next steps envisaged on the way towards the Nuclear Clock.
{"title":"‘Phase Transition’ in the ‘Thorium-Isomer Story’","authors":"P. Thirolf, B. Seiferle, L. Wense, I. Amersdorffer, D. Moritz, J. Weitenberg","doi":"10.5506/APhysPolB.51.561","DOIUrl":"https://doi.org/10.5506/APhysPolB.51.561","url":null,"abstract":"Given the drastic progress achieved during recent years in our knowledge on the decay and nuclear properties of the thorium isomer Th, the focus of research on this potential nuclear clock transition will turn in the near future from the nuclear physics driven ‘search and characterization phase’ towards a laser physics driven ‘consolidation and realization phase’. This prepares the path towards the ultimate goal of the realization of a nuclear frequency standard, the ‘Nuclear Clock’. This article briefly summarizes our present knowledge, focusing on recent achievements, and points to the next steps envisaged on the way towards the Nuclear Clock.","PeriodicalId":7060,"journal":{"name":"Acta Physica Polonica B","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48695710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-06DOI: 10.5506/APhysPolB.52.1209
Abdaljalel Alizzi, Abhijit Sen, Z. Silagadze
A bound state of muon and anti-muon (true muonium or dimuonium), although predicted long ago [1–4], has never been observed experimentally. Many mechanisms for the production of dimuonium have been proposed in the literature. Dimuonium can be formed in fixed-target experiments [5–9], in electron-positron collisions [1, 10–12], in elementary particle decays [13–19], in a quark-gluon plasma [20, 21], in relativistic heavy ion collisions [21–23], in an astrophysical context [24], or in experiments with ultra-slow muon beams [25, 26]. As part of the first stage of the expensive and long-term super charm-tau factory project, Budker Institute of Nuclear Physics (Novosibirsk) is currently developing plans to build an inexpensive, low-energy μμ-tron machine [27]. Apart from purely accelerator studies, the μμ-tron will make it possible to produce and investigate dimuonium experimentally. Studying the interactions of dimuonium with ordinary atoms as it passes through the foil is an integral part of the planned experiments. Elementary atoms, such as dimuonium, when passing through the foil interact with ordinary atoms predominantly via the Coulomb potential [28–30]. Such an interaction is treated in terms of atomic form factors, and a comprehensive review of atomic form factor calculations can be found in [31]. General analytical formulas for calculating the form factor of a hydrogen-like atom were obtained in [32] by grouptheoretical methods. However, these formulas have a somewhat complicated form, requiring time-consuming calculations for each value of a transfer momentum [33]. A more convenient set of formulas was developed in [33, 34] and implemented as a FORTRAN program in [35]. Based on the mathematical results obtained in [36], in this article we present an alternative method for calculating the form factor, which in some sense complements the method presented in [33, 34]. As a byproduct of this reaearch, some trigonometric identities involving Chebyshev polynomials of the second kind were obtained in [37]. Throughout the paper, we use dimuonium atomic units, in which c = h̄ = 1, the unit of mass is 12mμ (reduced mass in the dimuonium atom), and the unit of length is the radius of the first Bohr orbit in dimuonium: aB = 2 me mμ a0 ≈ 512 fm, where a0 ≈ 5.29× 10 m is the usual Bohr radius. Although the motivation for the article was Novosibirsk dimuonium program, we emphasize that the results obtained are in fact of much broader interest, mainly in atomic physics, see Devangan’s review article [31].
{"title":"Alternative Implementation of Atomic Form Factors","authors":"Abdaljalel Alizzi, Abhijit Sen, Z. Silagadze","doi":"10.5506/APhysPolB.52.1209","DOIUrl":"https://doi.org/10.5506/APhysPolB.52.1209","url":null,"abstract":"A bound state of muon and anti-muon (true muonium or dimuonium), although predicted long ago [1–4], has never been observed experimentally. Many mechanisms for the production of dimuonium have been proposed in the literature. Dimuonium can be formed in fixed-target experiments [5–9], in electron-positron collisions [1, 10–12], in elementary particle decays [13–19], in a quark-gluon plasma [20, 21], in relativistic heavy ion collisions [21–23], in an astrophysical context [24], or in experiments with ultra-slow muon beams [25, 26]. As part of the first stage of the expensive and long-term super charm-tau factory project, Budker Institute of Nuclear Physics (Novosibirsk) is currently developing plans to build an inexpensive, low-energy μμ-tron machine [27]. Apart from purely accelerator studies, the μμ-tron will make it possible to produce and investigate dimuonium experimentally. Studying the interactions of dimuonium with ordinary atoms as it passes through the foil is an integral part of the planned experiments. Elementary atoms, such as dimuonium, when passing through the foil interact with ordinary atoms predominantly via the Coulomb potential [28–30]. Such an interaction is treated in terms of atomic form factors, and a comprehensive review of atomic form factor calculations can be found in [31]. General analytical formulas for calculating the form factor of a hydrogen-like atom were obtained in [32] by grouptheoretical methods. However, these formulas have a somewhat complicated form, requiring time-consuming calculations for each value of a transfer momentum [33]. A more convenient set of formulas was developed in [33, 34] and implemented as a FORTRAN program in [35]. Based on the mathematical results obtained in [36], in this article we present an alternative method for calculating the form factor, which in some sense complements the method presented in [33, 34]. As a byproduct of this reaearch, some trigonometric identities involving Chebyshev polynomials of the second kind were obtained in [37]. Throughout the paper, we use dimuonium atomic units, in which c = h̄ = 1, the unit of mass is 12mμ (reduced mass in the dimuonium atom), and the unit of length is the radius of the first Bohr orbit in dimuonium: aB = 2 me mμ a0 ≈ 512 fm, where a0 ≈ 5.29× 10 m is the usual Bohr radius. Although the motivation for the article was Novosibirsk dimuonium program, we emphasize that the results obtained are in fact of much broader interest, mainly in atomic physics, see Devangan’s review article [31].","PeriodicalId":7060,"journal":{"name":"Acta Physica Polonica B","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42434013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-14DOI: 10.5506/APhysPolB.52.1339
F. Klinkhamer
It has been argued that the bosonic large- N master field of the IIB matrix model can give rise to an emergent classical spacetime. In a re-cent paper, we have obtained solutions of a simplified bosonic master-field equation from a related matrix model. In this simplified equation, the ef-fects of dynamic fermions were removed. We now consider the full bosonic master-field equation from a related supersymmetric matrix model for dimensionality D = 3 and matrix size N = 3 . In this last equation, the effects of dynamic fermions are included. With an explicit realization of the random constants entering this algebraic equation, we establish the existence of nontrivial solutions. The small matrix size, however, does not allow us to make a definitive statement as to the appearance of a diagonal/band-diagonal structure in the obtained matrices.
{"title":"Solutions of the Bosonic Master-Field Equation from a Supersymmetric Matrix Model","authors":"F. Klinkhamer","doi":"10.5506/APhysPolB.52.1339","DOIUrl":"https://doi.org/10.5506/APhysPolB.52.1339","url":null,"abstract":"It has been argued that the bosonic large- N master field of the IIB matrix model can give rise to an emergent classical spacetime. In a re-cent paper, we have obtained solutions of a simplified bosonic master-field equation from a related matrix model. In this simplified equation, the ef-fects of dynamic fermions were removed. We now consider the full bosonic master-field equation from a related supersymmetric matrix model for dimensionality D = 3 and matrix size N = 3 . In this last equation, the effects of dynamic fermions are included. With an explicit realization of the random constants entering this algebraic equation, we establish the existence of nontrivial solutions. The small matrix size, however, does not allow us to make a definitive statement as to the appearance of a diagonal/band-diagonal structure in the obtained matrices.","PeriodicalId":7060,"journal":{"name":"Acta Physica Polonica B","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45777196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-02DOI: 10.5506/APhysPolB.52.575
F. Jegerlehner
I am considering Veltman’s “The Infrared–Ultraviolet Connection” addressing the issue of quadratic divergences and the related huge radiative correction predicted by the electroweak Standard Model (SM) in the relationship between the bare and the renormalized theory, commonly called “the hierarchy problem” which usually is claimed that this has to be cured. After the discovery of the Higgs particle at CERN, which essentially completed the SM, an amazing interrelation of the leading interaction strengths of the gauge bosons, the top quark, and the Higgs boson showed up amounting that the SM allows for a perturbative extrapolation of the running couplings up to the Planck scale. The central question concerns the stability of the electroweak vacuum, which requires that the running Higgs self-coupling stays positive. Although several evaluations seem to favor the meta-stability within the experimental and theoretical parameter-uncertainties, one should not exclude the possibility that other experiments and improved matching conditions will be able to establish the absolute stability of the SM vacuum in the future. I will discuss the stable vacuum scenario and its impact on early cosmology, revealing the Higgs boson as the inflaton. It turns out that the Standard Model’s presumed “hierarchy problem” and similarly the “cosmological constant problem” resolve themselves when we understand the SM as a low-energy effective tail that is emergent from a cutoff-medium at the Planck scale. “The Infrared–Ultraviolet Connection” conveyed by the Higgs boson mass renormalization appears in a new light when the energy dependence of the SM couplings is taken into account.
{"title":"The Standard Model of Particle Physics as a Conspiracy Theory and the Possible Role of the Higgs Boson in the Evolution of the Early Universe","authors":"F. Jegerlehner","doi":"10.5506/APhysPolB.52.575","DOIUrl":"https://doi.org/10.5506/APhysPolB.52.575","url":null,"abstract":"I am considering Veltman’s “The Infrared–Ultraviolet Connection” addressing the issue of quadratic divergences and the related huge radiative correction predicted by the electroweak Standard Model (SM) in the relationship between the bare and the renormalized theory, commonly called “the hierarchy problem” which usually is claimed that this has to be cured. After the discovery of the Higgs particle at CERN, which essentially completed the SM, an amazing interrelation of the leading interaction strengths of the gauge bosons, the top quark, and the Higgs boson showed up amounting that the SM allows for a perturbative extrapolation of the running couplings up to the Planck scale. The central question concerns the stability of the electroweak vacuum, which requires that the running Higgs self-coupling stays positive. Although several evaluations seem to favor the meta-stability within the experimental and theoretical parameter-uncertainties, one should not exclude the possibility that other experiments and improved matching conditions will be able to establish the absolute stability of the SM vacuum in the future. I will discuss the stable vacuum scenario and its impact on early cosmology, revealing the Higgs boson as the inflaton. It turns out that the Standard Model’s presumed “hierarchy problem” and similarly the “cosmological constant problem” resolve themselves when we understand the SM as a low-energy effective tail that is emergent from a cutoff-medium at the Planck scale. “The Infrared–Ultraviolet Connection” conveyed by the Higgs boson mass renormalization appears in a new light when the energy dependence of the SM couplings is taken into account.","PeriodicalId":7060,"journal":{"name":"Acta Physica Polonica B","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43888564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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